Abian, Alexander, 1923-

Set theory
Algebra, Boolean

Box

Folder

Title

Dates

1

1

Biographical information

1923-1999

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 Sub-Covering 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 Sub-sets 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 Semi-Simple 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 Semi-Simple 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 C-Algebra"

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 2-Cell"

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 n-Space"

1962

1

67

"Forcing VIA Compatibility"

1985

1

68

"Four-Coloring of Infinite Maps"

1978

1

69

"Free p-Rings and the Two Countable Chain Conditions"

1980

1

70

"Functional Invariants of a Linear Homogeneous Integro-Differential 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 Sub-sets of Partially Ordered Sets"

1994

1

76

"Generic Sub-sets 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

"K-Inductive Boolean Algebras and the Existence of Special Ultra-filters"

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 n-Cell"

1962

1

109

"New Proof of Ramsey's Theorem"

1974

1

110

"New Proof of the Fundamental Theorem of Algebra"

1986

1

111

"Non-Existence of Ordered Sets with Denumerable Many Sub-sets"

1976

1

112

"Nonexistence of Monomolecular Generic Sets"

1984

113

"Nonisomorphic Atoms Boolean Algebras"

1973

1

114

"Nonmetrizability of Uncountable Well-ordered 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 Hyper-atom 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 Set-theoretical 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 Pre-p-Rings"

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
f(x,y,y ⁽¹⁾ ,…y⁽ⁿ⁾)=0"

1958

1

164

"On the Solution of the Differential Equation f(x,y,y¹)=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 Sub-base 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

"P-Model 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  p-Rings and Solvability of  Systems of Polynomial Equations over I_p"

1971

1

189

"Prime Ideals of Sub-rings 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 2-Cell"

1961

1

193

"Proof of a Rasiowa-Sikorski Theorem via Complete Sequences

1975

1

194

"Proof of a Theorem of Rasiowa-Sikorski"

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

"Pseudo-Inductive Sub-sets 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 Sub-covering Property"

1982

1

209

"Rings of Real Valued Functions and the Finite Sub-Covering 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

"Set-Theoretical 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 Fraenkel-Mostowski 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 Power-Set"

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 Skew-Symmetric 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 Sub-coverable Extensions"

1977

1

234

"Special Partition of the Reals into Nonmeasurable Sub-sets"

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 A-Inductive 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