Special Collections and University Archives
403 Parks Library  701 Morrill Road
Iowa State University
Ames, IA 500112102
RS 13/14/53
Alexander Abian (19231999)
Papers, 19231999, undated
creator:  Abian, Alexander, 1923 
title:  Papers 
dates:  19231999, undated 
extent:  1.3 linear feet (1 records center carton) 
collection number:  RS 13/14/53 
repository:  University Archives, Special Collections Department, Iowa State University 
language:  English 
access:  Open for research 
publication rights:  Consult Special Collections and University Archives 
preferred citation:  Alexander Abian Papers, RS 13/14/53, Iowa State University Library Special Collections and University Archives. 
people, families, and corporate bodies:  Abian, Alexander, 1923 
places:  
subjects:  Set theory 
genres: 
Alexander Abian, born on January 1, 1923, was a Professor (19661988) in the Department of Mathematics at Iowa State University who received his B.S. (1946) from Tehran University, M.S. (1954) from the University of Chicago, and Ph.D. (1956) from the University of Cincinnati. His main areas of study were the foundations of mathematics, set theory, algebra, mathematical logic, and Boolean rings. This collection includes biographical information, news clippings, and publications. The publications cover subjects of his interest such as Boolean rings, set theory, fixed point theorem, and Taylor's theorem. 
Alexander Abian was born January 1, 1923, in Armenia. He received his B.S. (1946) from Tehran University, a M.S. (1954) from University of Chicago and a Ph.D. (1956) from the University of Cincinnati. Abian served on the faculties of the University of Tennessee (19561957) and Queens College (19571959) as an Instructor of Mathematics. He was an Assistant Professor (19591962) in mathematics at the University of Pennsylvania and an Associate Professor (19621967) of mathematics at Ohio State University. In 1966, Abian joined the faculty as a Professor (19661988) in the Department of Mathematics at Iowa State University. Abian's main areas of study were the foundations of mathematics, set theory, algebra, mathematical logic, and Boolean rings. He published over 91 papers for international mathematical journals. He was also active in several professional organizations, including serving as Chair of the Mathematics Colloquia Committee and member of the American Mathematical Society He and his wife Thelma had three children: Rimma, Lisa, and Andrew. Alexander Abian died on July 24, 1999. 
This collection (19571999) includes biographical information, news clippings, and publications by Alexander Abian. The publications concern subjects such as Boolean rings, set theory, fixed point theorem, and Taylor's theorem. 
This collection is arranged alphabetically. 
Box 
Folder 
Title 
Dates 
1 
1 
Biographical information 
19231999 
1 
2 
"Addendum to Order in a Special Class of Rings and a Structure Theorem" 
1976 
1 
3 
"Additive and Linear Mappings in Normal Vector Spaces" 
1998 
1 
4 
"Angle Between Two Sets and Their Inner Product in Any Banach Space" 
1990 
1 
5 
"Application of Ramsey's Theorem" 
1974 
1 
6 
"Basis of Abelian Groups" 
1994 
1 
7 
"Boolean Functions and Equations" 
1974 
1 
8 
"Boolean Rings of Sets Describing Their Own Stone Representation" 
1976 
1 
9 
"Boolean Rings of Sets with Finite SubCovering Property" 
1969 
1 
10 
"Boolean Rings with Isomorphisms Preserving Suprema and Infima" 
1970 
1 
11 
"Calculus Must Consist of the Study of Real Numbers in Their Decimal Representation" 
1981 
1 
12 
"Cantor Subsets and Outer Measures of Sets" 
1999 
1 
13 
"Cantor Ternary Set and Measurability of Hamel Bases" 
1998 
1 
14 
"Cardinality of Ordinal Exponentiation 1972" 

1 
15 
"Cardinality of Powersets in Finite Models of the Powerset Axiom" 
1991 
1 
16 
"Category of Denumerable Atomless Boolean Rings" 
1972 
1 
17 
"Coefficients of the Laurent Expansion of Analytic Functions" 
1976 
1 
18 
"Coefficients of the Laurent Series Expansion of Real Analytic Functions" 
1993 
1 
19 
"Common Points of Families of Normal Functions" 
1973 
1 
20 
"Compact Partially Ordered Sets and Compactification of Partially Ordered Sets" 
1982 
1 
21 
"Compact Partially Ordered Sets" 
1980 
1 
22 
"Compactness of the Hyperplane Topology" 
1974 
1 
23 
"Compactness of the Product of Two Compact Spaces without the Axiom of Choice" 
1996 
1 
24 
"Compactness of the Product Topology and the Solvability of Infinite Systems of Infinite Linear Equations" 
1983 
1 
25 
"Complete Prime Ideals of Boolean Rings" 
1972 
1 
26 
"Completeness of the Generalized Propositional Calculus" 
1970 
1 
27 
"Conditional Completion of Boolean Rings by Lower Cuts" 
1975 
1 
28 
"Conditionally Complete and Conditionally Orthogonally Complete Rings" 
1980 
1 
29 
"Consistency and Independence of Suslin's Hypothesis" 
1989 
1 
30 
"Consistency of the Continuum Hypothesis via Synergistic Models" 
1973 
1 
31 
"Continuity Based on Convergence and Lower Complete Disruptive Lattices Instead of Directed Sets" 
1971 
1 
32 
"Contrast Between Complex and Real Valued Taylor Series" 
1974 
1 
33 
"Convergent Subsequences of Generalized Sequences" 
1973 
1 
34 
"Convolution Product and Fourier Transform" 
1998 
1 
35 
"Decomposition of Commutative SemiSimple Rings into Direct Product of Integral Domains" 
1973 
1 
36 
"Definition and Construction of Free Algebras Revisited" 
1982 
1 
37 
"Derivatives at Bounty Points" 
1998 
1 
38 
"Deserved Set Axioms for Topology" 
1970 
1 
39 
"Determinate Version of Taylor Theorems and Some Generalizations" 
1984 
1 
40 
"Direct Product Decomposition of Commutative SemiSimple Rings" 
1970 
1 
41 
"Direct product Decomposition of Zero Product Associative Rings Without Nilpotent Elements" 
1978 
1 
42 
"Direct Proof of Taylor Theorems" 
undated 
1 
43 
"Direct Sum Decomposition of Atomic and Orthogonally Complete Rings" 
1970 
1 
44 
"Dyadic Matrices and Wallman Compactification" 
1979 
1 
45 
"E Complete and D Generic Filters of Partially Ordered Sets" 
1990 
1 
46 
"El Teorema de Taylor" 
1989 
1 
47 
"Equations of the Best Fitting Lines" 
1985 
1 
48 
"Equivalent of the Axiom of Choice in Finite Models of the Powerset Axiom" 
1990 
1 
49 
"Essentials of Measure and Integration" 
1986 
1 
50 
"Everywhere Defined Unbounded Invertible Linear Operator in a Hilbert Space" 
undated 
1 
51 
"Everywhere Differentiable Absolutely Continuous Function Whose Derivative Is Not Riemann Integrable" 
1991 
1 
52 
"Example of Commutative CAlgebra" 
1997 
1 
53 
"Example of a Nonmeasurable Set" 
1968 
1 
54 
"Examples of Generalized Sheffer Functions" 
1967 
1 
55 
"Existence of Prime Ideals and Ultrafilters in Partially Ordered Sets" 
1988 
1 
56 
"Expansions into Iterated Square Roots" 
1993 
1 
57 
"Family of Analytic Functions Whose Members Have Equal Number of Zeros" 
1981 
1 
58 
"Fixed Point Theorem" 
1968 
1 
59 
"Fixed Point Theorem Equivalent to the Axiom of Choice" 
1985 
1 
60 
"Fixed Point Theorem for Image Intersecting Mappings" 
1979 
1 
61 
"Fixed point Theorem for Mappings" 
1968 
1 
62 
"Fixed point Theorem for Nonincreasing Mappings" 
1969 
1 
63 
"Fixed Point Theorem for the Closed 2Cell" 
1962 
1 
64 
"Fixed Point Theorems of the Mappings of Partially Ordered Sets" 
1971 
1 
65 
"Fixed Points and Covering Under Continuous Mappings of a Spherical Shell" 
1962 
1 
66 
"Fixed Points of Continuous Mappings into Euclidean nSpace" 
1962 
1 
67 
"Forcing VIA Compatibility" 
1985 
1 
68 
"FourColoring of Infinite Maps" 
1978 
1 
69 
"Free pRings and the Two Countable Chain Conditions" 
1980 
1 
70 
"Functional Invariants of a Linear Homogeneous IntegroDifferential Equation" 
1958 
1 
71 
"Fundamental Fixed Point Theorem Revisited" 
1980 
1 
72 
"Fundamental Property of Inductive Partially Ordered Sets" 
1987 
1 
73 
"General Definition of Convergence, Continuity, Differentiability and Integrability" 
1958 
1 
74 
"Generalizing the Generalized Mean Value Theorem" 
1981 
1 
75 
"Generic Chain and Generic Directed Subsets of Partially Ordered Sets" 
1994 
1 
76 
"Generic Subsets of Separate Partially Ordered Sets" 
1971 
1 
77 
"Geometric Proof of the Lebesgue Differentiation Theorem" 
1990 
1 
78 
"Honest Subgroups of Abelian Groups" 
1963 
1 
79 
"How to Remember and Use Stokes' Theorem Easily" 
1998 
1 
80 
"Hurwitz Theorem Implies Rouché's Theorem" 
1977 
1 
81 
"Identity Theorem for Analytic Functions" 
1974 
1 
82 
"Inductive Boolean Algebras and Their Special Prime Ideals" 
1979 
1 
83 
"Infinite Matrices with Orthonormal Rows" 
1987 
1 
84 
"Infinitely Differentiable Functions with Prescribed Derivations at a Point" 
1983 
1 
85 
"Inner Product and Orthonormalization in l^{p} Spaces and Solution of Infinite Systems on Infinite Linear Equations" 
1990 
1 
86 
"International Journal of Mathematical Education of Science and Technology" 
1991 
1 
87 
"Iterative Construction of Bases for Finitely Generated Models over Principal Ideal Domains" 
1985 
1 
88 
"Iterative Construction of Bases for Finitely Generated Modules over Principal Ideal Domains" 
1991 
1 
89 
"Jacobson's Theorem for Alternative Rings" 
1979 
1 
90 
"Jordan Canonical Forms of Matrices AB and BA" 
1990 
1 
91 
"KInductive Boolean Algebras and the Existence of Special Ultrafilters" 
1979 
1 
92 
"Laurent Series Obtained by Long Division" 
1980 
1 
93 
"Laurent Series Obtained by Long Division" 
1985 
1 
94 
"Lebesgue Integral Defined in the Manner of Riemann" 
1997 
1 
95 
"Lemma for Incompleteness and Nonprincipal Ultrafilters" 
1989 
1 
96 
"Linear Extensions of Partial Orders" 
1974 
1 
97 
"Mathematical Justification of the Laws of Classical Implication" 
1983 
1 
98 
"Measurable Outer Kernels of Sets" 
1982 
1 
99 
"Method of Synergistic Models" 
1972 
1 
100 
"Model for the Generalized Continuum Hypothesis with Three Infinite Cardinals" 
1974 
1 
101 
"Molecules of a Partially Ordered Set" 
1981 
1 
102 
"Most Direct Proof of Compactness of the Product of Compact Spaces" 
1990 
1 
103 
"Natural Right and the Natural Left Inverses of Rectangular Matrices" 
1990 
1 
104 
"Natural Topology of the Space of Sequence on Two Symbols" 
1966 
1 
105 
"Negation and Quasi Complementation Based on Incompatibility" 
1986 
1 
106 
"Nest Complete Accumulation Point Compactness of the Product of Topological Spaces" 
1996 
1 
107 
"New Construction of Free Groups" 
1980 
1 
108 
"New Fixed Point Theorem for Continuous Maps of the Closed nCell" 
1962 
1 
109 
"New Proof of Ramsey's Theorem" 
1974 
1 
110 
"New Proof of the Fundamental Theorem of Algebra" 
1986 
1 
111 
"NonExistence of Ordered Sets with Denumerable Many Subsets" 
1976 
1 
112 
"Nonexistence of Monomolecular Generic Sets" 
1984 

113 
"Nonisomorphic Atoms Boolean Algebras" 
1973 
1 
114 
"Nonmetrizability of Uncountable Wellordered Spaces" 
1981 
1 
115 
"Nonstandard Models for Arithmetic and Analysis" 
1972 
1 
116 
"Nowhere Differentiable and Except on a Denumerable Set Everywhere Continuous Function" 
1961 
1 
117 
"Number of Prime Ideals of a p Ring" 
1979 
1 
118 
"On a Property of Countable Partitioning of the Continuum Without the Use of Koenig's Lemma" 
1980 
1 
119 
"On a Property of Finite Truncations of the Laurent Series of Analytic Functions" 
1980 
1 
120 
"On a Useful Economy in the Formation of Riemann Sums" 
1978 
1 
121 
"On Borel, Baire, and Lebesgue Sets" 
1979 
1 
122 
"On Comparability of Sets" 
1963 
1 
123 
"On Definitions of Cut and Completion of Partially Ordered Sets" 
1968 
1 
124 
"On Foundations of Projective Differential Geometry" 
1957 

125 
"On Generic Sets and their Products" 
1972 
1 
126 
"On Inaccessible Cardinal Numbers" 
1969 
1 
127 
"On Measurability of Uncountable Unions of Measurable Sets" 
1992 
1 
128 
"On Properties of Derivatives of Continuous Functions" 
1992 
1 
129 
"On Representation of Partially Ordered Sets" 
1966 
1 
130 
"On Representations of Partially Ordered Sets" 
1967 
1 
131 
"On Set Theoretical Models and the Independence of Set Theoretical Axioms" 
1971 
1 
132 
"On Solvability of Infinite Systems Polynomial Equations over Finite Ring" 
1972 
1 
133 
"On Some Fundamental Properties of Cofinality of Ordinal Numbers" 
1970 
1 
134 
"On the Associativity and Communitativity of Multiplication of Infinite Matrices" 
1988 
1 
135 
"On the Bounds of the Minimal Length of Sequences Representing Simply Ordered Sets" 
1966 
1 
136 
"On the Cardinality of the Set of Prime Ideals of Nonatomic Boolean Rings" 
1971 
1 
137 
"On the Cardinally of Some Powersets" 
1978 
1 
138 
"On the Cartesian Product of Sets" 
1963 
1 
139 
"On the Confinality of Ordinal Numbers" 
1969 
1 
140 
"On the Consistency and Independence of Some Set Theoretical Axioms" 
1978 
1 
141 
"On the Consistency of the Generalized Continuum Hypothesis" 
1972 
1 
142 
"On the Countability of a Set of Real Numbers" 
1986 
1 
143 
"On the Definition of a Hyperatom of a Ring" 
1979 
1 
144 
"On the Difference of the Number of Zeros and Poles of the Members of Convergent Sequences of Meromorphic Functions" 
1982 
1 
145 
"On the Equipollence of Sets" 
1964 
1 
146 
"On the Existence of an Empty Set in Settheoretical Models" 
1966 
1 
147 
"On the Existence of Compactification of Partial Ordered Sets" 
1988 
1 
148 
"On the Exponentiation of Transfinite Cardinals" 
1971 
1 
149 
"On the Independence of Set Theoretical Axioms" 
1969 
1 
150 
"On the Independence of the Axiom of Choice" 
1972 
1 
151 
"On the Index of Nilpotency of Some Nil Algebras" 
1963 
1 
152 
"On the Isomorphism of Partially Ordered Sets" 
1970 
1 
153 
"On the Isomorphisms of Boolean Rings" 
1970 
1 
154 
"On the Lengths of Bases of a Finitely Generated Abelian Group" 
1964 
1 
155 
"On the Minimal Length of Sequences Representing Simply Ordered Sets" 
1967 
1 
156 
"On the Restriction in the Formulation of the Axiom Scheme of Replacement of ZF" 
1978 
1 
157 
"On the Similarity of Partially Ordered Sets" 
1970 
1 
158 
"On the Solution of an Implicit Equation" 
1959 
1 
159 
"On the Solution of Arbitrary System of Linear Equations" 
1960 
1 
160 
"On the Solution of PrepRings" 
1964 
1 
161 
"On the Solution of Simultaneous First Order Implicit Differential Equations" 
1959 
1 
162 
"On the Solution of Simultaneous Implicit Equations" 
1959 
1 
163 
"On the Solution of the Differential Equation 
1958 
1 
164 
"On the Solution of the Differential Equation f(x,y,y^{1})=0" 
1959 
1 
165 
"On the Solution of the Equation g(x)=0" 
1959 
1 
166 
"On the Solvability of Arbitrary Large Infinite Systems of Infinite Linear Equations" 
1989 
1 
167 
"On the Solvability of Infinite Systems of Boolean Polynomial Equations" 
1970 
1 
168 
"On the Stranded Model Hypothesis of ZF" 
1975 
1 
169 
"On the Use of More Than Two Elements Boolean Valued Models" 
1975 
1 
170 
"On Transfinite Splittings on Infinite Sets" 
1989 
1 
171 
"On Truncations of Entire Transcendental Functions" 
1981 
1 
172 
"On Two Theorems of A. Abian" 
1975 
1 
173 
"On Uniform Structures" 
1965 
1 
174 
"On Various Characterizations of Compactness" 
1992 
1 
175 
"Order in a Special Class of Rings and a Structure Theorem" 
1975 
1 
176 
"Order Relation in Rings Without Nilpotent Elements" 
1974 
1 
177 
"Outer and Inner Measures of a Nonmeasurable Set" 
1970 
1 
178 
"Partial Order Generalization of Alexander's Subbase Theorem" 
1980 
1 
179 
"Partially Ordered Sets of Sequences and the Related Boolean Algebras" 
1983 
1 
180 
"Particular Equivalent of Picard's Little Theorem" 
1997 
1 
181 
"Partition of Nondenumerable Closed Sets of Reals" 
1974 
1 
182 
"Passages Between Finite and Infinite" 
1978 
1 
183 
"PModel and the Consistency and the Independence of the Axiom of Regularity" 
1972 
1 
184 
"Practical Evaluation of the Minimum and the Maximum Moduli of Zeros of Polynomials 
1985 
1 
185 
"Precise Annuli Containing the Zeros of Polynomials" 
1981 
1 
186 
"Precise Annulus Containing all the Zeros of a Polynomial" 
1983 
1 
187 
"Preliminary To Forcing Set Theory of the Standard and Minimal Standard Model of ZF" 
1977 
1 
188 
"Prime Ideal Theorem for pRings and Solvability of Systems of Polynomial Equations over I_{p}" 
1971 
1 
189 
"Prime Ideals of Subrings of Boolean Rings" 
1971 
1 
190 
"Prime Ideals of the Boolean of Internals" 
1979 
1 
191 
"Products of Cantor's Discontinuum" 
1985 
1 
192 
"Proof and Extension of Brouwer's Fixed Point Theorem for the Closed 2Cell" 
1961 
1 
193 
"Proof of a RasiowaSikorski Theorem via Complete Sequences 
1975 
1 
194 
"Proof of a Theorem of RasiowaSikorski" 
1972 
1 
195 
"Proof of Rado's Theorem" 
1980 
1 
196 
"Proof of the Arithmetic Geometric Mean Inequality" 
1993 
1 
197 
"Property of Baire First Category Sets" 
1975 
1 
198 
"Property Of Entire Transcendental Functions" 
1976 
1 
199 
"PseudoInductive Subsets of Partially Ordered Sets" 
1989 
1 
200 
"Purely Number Theoretic Attempt to Prove Picard's Theorems 
1983 
1 
201 
"Rado's Theorem and Solvability of Systems of Equations" 
1973 
1 
202 
"Receding Sequences of Sets Ordinals" 
1975 
1 
203 
"Regular Spaces and Abian Structures" 
undated 
1 
204 
"Representation and Completion of Partially Ordered Sets by Dyadic Sequences" 
1978 
1 
205 
"Representation of Partially and Simply Ordered Sets by Terminating Sequences" 
1966 
1 
206 
"Representation of Simply Ordered Sets and the Generalization Continuum Hypothesis" 
1967 
1 
207 
"Retrieving a Topological Space From Its Lattice of Open Sets" 
1992 
1 
208 
"Rings of Bound Real Valued Functions and the Finite Subcovering Property" 
1982 
1 
209 
"Rings of Real Valued Functions and the Finite SubCovering Property" 
1979 
1 
210 
"Rings Satisfying Wilson's Equality" 
1976 
1 
211 
"Rings Without Nilpotent Elements" 
1975 
1 
212 
"Row Orthonormal Infinite Square Matrices" 
1982 
1 
213 
"SetTheoretical Canonicals Models" 
1972 
1 
214 
"Short Proof of a Stronger Version of Popruźenko's Theorem" 
1966 
1 
215 
"Short Proof of Stone's Theorem" 
1970 
1 
216 
"Simple Proof of a Weaker Form of Stirling's Formula" 
1990 
1 
217 
"Simple Proof of the Subgroup Theorem for Free Groups" 
1984 
1 
218 
"Simplest Example of Nonmeasurable Set" 
1976 
1 
219 
"Simplified Version of FraenkelMostowski Model for the Independence of the Axiom" 
1979 
1 
220 
"Simultaneous Constitution of Similar Matrices and the Similarity Transformation" 
1988 
1 
221 
"Solutions and Representations by Iterated Radicals" 
1993 
1 
222 
"Solvability of Infinite Systems of Polynomial Equations over the Field of Complex Numbers" 
1985 
1 
223 
"Solvability of Infinite Systems of Linear Equations" 
1975 
1 
224 
"Solvability of Infinite Systems of Linear Equations Over Division Modules" 
1998 
1 
225 
"Solvability of Infinite Systems on Infinite Linear Equations" 
1982 
1 
226 
"Solvable Case of an Infinite System of Infinite Linear Equations and Two Examples of Applications" 
1983 
1 
227 
"Some Consequence of the Axiom of PowerSet" 
1965 
1 
228 
"Some Generalized Sheffer Functions" 
1965 
1 
229 
"Some Negative Determinants in Inner Product Spaces" 
1986 
1 
230 
"Some Properties of Row Orthonormal Infinite Square Matrices and Solvability of Infinite Systems of Infinite Equations" 
1983 
1 
231 
"Some Properties of SkewSymmetric Elements of a Ring" 
1958 
1 
232 
"Some Special Properties of Cofinality of Ordinal Numbers" 
1970 
1 
233 
"Special Class of Rings of Functions and Their Finitely Subcoverable Extensions" 
1977 
1 
234 
"Special Partition of the Reals into Nonmeasurable Subsets" 
1998 
1 
235 
"Stone Space of a Boolean Ring" 
1965 
1 
236 
"Sums of Infinitely Many Sequences" 
1998 
1 
237 
"Systems of Linear Equations and Model Theory" 
1987 
1 
238 
"Theorem Equivalent to Picard's Little Theorem and a Deviation of the Fundamental Theorem of Algebra" 
1997 
1 
239 
"Theorem Equivalent to the Fundamental Theorem of Algebra" 
1990 
1 
240 
"Theorem of Locally Connected Sets" 
1965 
1 
241 
"Theorem on Partially Ordered Sets with Applications To Fixed Point Theorems" 
1961 
1 
242 
"Topological Structures and Abian Structures" 
1978 
1 
243 
"Total Compactness of AInductive Partially Ordered Sets" 
1990 
1 
244 
"Two Basic Methods of Compactification of Dyadic Matrices by Row Extensions" 
1983 
1 
245 
"Two Methods of Construction of Free Boolean Algebras" 
1979 
1 
246 
"Two Properties of Free Boolean Algebras" 
1974 
1 
247 
"Two Theorems on Truncations of the Laurent Series" 
1981 
1 
248 
"Ultimate Proof of Rolle's Theorem" 
1979 
1 
249 
"Uniform Structure for Topological Spaces" 
1978 
1 
250 
"Unique Determination of Any Analytic Function of Two Real Variables from its Values Given on the Points of a Denumerable Set" 
1983 
1 
251 
"Unique Determination of any Harmonic Function From its Values Given on the Points of Two Convergent Sequences" 
1984 
1 
252 
"Unramified Forcing Preserving the Law of Double Negation" 
1987 
1 
253 
"Unsolvability of the Halting Problem for Turing Machines" 
1977 
1 
254 
"Use of Mitotic Ordinals in Cardinal Arithmetic" 
1972 
1 
255 
"Wallman Compactification and Matrices of Zeros and Ones" 
1979 
1 
256 
"Well Ordering of the Cartesian Product of Two Ordinals" 
1979 
1 
257 
"Zeros of Partial Sums of the Laurent Series of Analytic Functions" 
1981 