research overview
- Dr. Szendrei's research interests include the structure theory of finite algebras, commutator theory, classification results using clone theory, and applications of these techniques and results to problems in computer science.
- Contact Info
Szendrei, Agnes
Positions
- Professor Emerita/Emeritus, Mathematics
Research Areas
Research
keywords
- structure theory, commutator theory, clone theory, algebra algorithms
Publications
selected publications
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book
- Clones in universal algebra. Ed. 99. 1986
- Lectures in universal algebra. Ed. 43. 1986
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chapter
- Partial orders induced by quasilinear clones. 51-83. 2012
- A survey of clones closed under conjugation. 297-343. 2004
- Modules in general algebra. 41-53. 1998
- A survey on strictly simple algebras and minimal varieties. 209-239. 1992
- Symmetric algebras. 259-280. 1988
- Locally para-primal algebras. 367-399. 1987
- Demi-primal algebras with a single operation. 509-531. 1986
- Unary polynomials in algebras. II. 273-290. 1983
- On the idempotent reducts of modules. I, II. 753-780. 1982
- Algebras with doubly transitive automorphism groups. 521-535. 1981
- Clones of linear operations on finite sets. 693-738. 1981
- On weakly commuting operations. 373-380. 1979
- On affine modules. 457-Vol. 17. 1977
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conference proceeding
-
Rosenberg-Type Completeness Criteria for Subclones of Slupecki's Clone.
Proceedings of the International Symposium on Multiple Valued Logic.
349-354.
2012
- A COMPLETENESS CRITERION FOR SEMI-AFFINE ALGEBRAS. 314-319. 1992
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Rosenberg-Type Completeness Criteria for Subclones of Slupecki's Clone.
Proceedings of the International Symposium on Multiple Valued Logic.
349-354.
2012
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journal article
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Random models of idempotent linear Maltsev conditions. I. Idemprimality.
Algebra Universalis.
2020
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Is supernilpotence super nilpotence?.
Algebra Universalis.
2020
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Commutative Rings Whose Principal Ideals Have Unique Generators.
Springer Proceedings in Mathematics and Statistics.
1-9.
2020
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THE SUBPOWER MEMBERSHIP PROBLEM FOR FINITE ALGEBRAS WITH CUBE TERMS.
Logical Methods in Computer Science.
2019
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Varieties whose finitely generated members are free.
Algebra Universalis.
2018
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Cube term blockers without finiteness.
Algebra Universalis.
437-459.
2017
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Simpler Maltsev conditions for (weak) difference terms in locally finite varieties.
Algebra Universalis.
555-561.
2017
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Dualizable algebras with parallelogram terms.
Algebra Universalis.
497-539.
2016
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Growth rates of algebras, III: finite solvable algebras.
Algebra Universalis.
199-222.
2016
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GROWTH RATES OF ALGEBRAS, I: POINTED CUBE TERMS.
Journal of the Australian Mathematical Society.
56-94.
2016
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A FINITE BASIS THEOREM FOR DIFFERENCE-TERM VARIETIES WITH A FINITE RESIDUAL BOUND.
Transactions of the American Mathematical Society.
2115-2143.
2016
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Growth rates of algebras, II: Wiegold dichotomy.
International Journal of Algebra and Computation.
555-566.
2015
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Commuting Polynomial Operations of Distributive Lattices.
Order: a journal on the theory of ordered sets.
245-269.
2012
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The 3rd International Conference on Boolean Algebra, Lattice Theory, Universal Algebra, Set Theory and Set-theoretical Topology-BLAST 2010.
Order: a journal on the theory of ordered sets.
229-230.
2012
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An easy test for congruence modularity.
Algebra Universalis.
375-392.
2012
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CLONES OF ALGEBRAS WITH PARALLELOGRAM TERMS.
International Journal of Algebra and Computation.
2012
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Clones with finitely many relative R-classes.
Algebra Universalis.
109-159.
2011
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The submaximal clones on the three-element set with finitely many relative R-classes.
Discussiones Mathematicae - General Algebra and Applications.
7-7.
2010
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Equivalence of operations with respect to discriminator clones.
Discrete Mathematics.
673-685.
2009
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Clones of 2-step nilpotent groups.
Algebra Universalis.
491-512.
2008
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Clones closed under conjugation I: Clones with constants.
International Journal of Algebra and Computation.
7-58.
2008
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Clones of finite groups.
Algebra Universalis.
23-52.
2005
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Groups with identical subgroup lattices in all powers.
Journal of Group Theory.
385-402.
2004
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Chief factor sizes in finitely generated varieties.
Canadian Journal of Mathematics.
736-756.
2002
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Generating singular transformations.
Semigroup Forum.
441-448.
2001
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Collapsing permutation groups.
Algebra Universalis.
35-51.
2001
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The join of two minimal clones and the meet of two maximal clones.
Algebra Universalis.
161-178.
2001
- The classification of commutative minimal clones. Discussiones Mathematicae Algebra and Stochastic Methods. 147-178. 1999
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The residual character of varieties generated by strictly simple term minimal algebras.
Algebra Universalis.
269-288.
1999
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The relationship between two commutators.
International Journal of Algebra and Computation.
497-531.
1998
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Projectivity and isomorphism of strictly simple algebras.
Algebra Universalis.
45-56.
1998
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Self-rectangulating varieties of type 5.
International Journal of Algebra and Computation.
511-540.
1997
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A characterization of minimal locally finite varieties.
Transactions of the American Mathematical Society.
1749-1768.
1997
- Nearly-idempotent plain algebras are indeed nearly idempotent plain algebras. Mathematica Slovaca. 391-403. 1996
- Expansions of minimal varieties. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 659-679. 1995
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MAXIMAL NON-AFFINE REDUCTS OF SIMPLE AFFINE ALGEBRAS.
Algebra Universalis.
144-174.
1995
- Strongly abelian minimal varieties. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 25-42. 1994
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TERM MINIMAL ALGEBRAS.
Algebra Universalis.
439-477.
1994
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THE SET OF TYPES OF A FINITELY GENERATED VARIETY.
Discrete Mathematics.
1-20.
1993
- Non-finitely based finite groupoids generating minimal varieties. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 593-600. 1993
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SIMPLE ABELIAN ALGEBRAS.
Journal of Algebra.
408-424.
1992
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THE PRIMAL ALGEBRA CHARACTERIZATION THEOREM REVISITED.
Algebra Universalis.
41-60.
1992
- A classification of strictly simple algebras with trivial subalgebras. Demonstratio Mathematica. 149-173. 1991
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SIMPLE SURJECTIVE ALGEBRAS HAVING NO PROPER SUBALGEBRAS.
Journal- Australian Mathematical Society Series a.
434-454.
1990
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LYNDON GROUPOID IS NOT INHERENTLY NONFINITELY BASED.
Algebra Universalis.
254-260.
1990
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EVERY IDEMPOTENT PLAIN ALGEBRA GENERATES A MINIMAL VARIETY.
Algebra Universalis.
36-39.
1988
- IDEMPOTENT ALGEBRAS WITH RESTRICTIONS ON SUBALGEBRAS. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 251-268. 1987
- SUBMAXIMAL CLONES WITH A PRIME-ORDER AUTOMORPHISM. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 29-48. 1985
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DEMI-PRIMAL ALGEBRAS.
Algebra Universalis.
117-128.
1984
- DEGREES OF CLONES AND RELATIONS. Houston Journal of Mathematics. 545-580. 1983
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SHORT MAXIMAL-CHAINS IN THE LATTICE OF CLONES OVER A FINITE-SET.
Mathematische Nachrichten.
43-58.
1983
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A new proof of the McKenzie-Gumm theorem.
Algebra Universalis.
144-144.
1982
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ALGEBRAS OF PRIME CARDINALITY WITH A CYCLIC AUTOMORPHISM.
Archiv der Mathematik.
417-427.
1982
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AUTOMORPHISM-GROUPS AND FUNCTIONAL COMPLETENESS.
Algebra Universalis.
385-400.
1982
- CORRECTION. Algebra Universalis. U143-U143. 1982
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A NEW PROOF OF THE MCKENZIE-GUMM THEOREM.
Algebra Universalis.
133-135.
1981
- Algebras with $p$-uniform principal congruences. Studia Scientiarum Mathematicarum Hungarica. 229-235. 1981
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IDENTITIES IN IDEMPOTENT AFFINE ALGEBRAS.
Algebra Universalis.
172-199.
1981
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IDENTITIES SATISFIED BY CONVEX LINEAR-FORMS.
Algebra Universalis.
103-122.
1981
- Independent basis for the identities of entropic groupoids. Commentationes Mathematicae Universitatis Carolinae. 71-85. 1981
- Sl upecki-type criteria for quasilinear functions over a finite-dimensional vector space. 601-611. 1981
- On closed classes of quasilinear functions. Czechoslovak Mathematical Journal. 498-509. 1980
- Remarks on a paper of L. Szabó and Á. Szendrei: “Almost all algebras with triply transitive automorphism groups are functionally complete” [Acta Sci. Math. (Szeged) bf 41 (1979), no. 3-4, 391–402; MR 81g:08006a]. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 95-98. 1980
- ALMOST ALL ALGEBRAS WITH TRIPLY TRANSITIVE AUTOMORPHISM-GROUPS ARE FUNCTIONALLY COMPLETE. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 391-402. 1979
- On closed sets of linear operations over a finite set of squarefree cardinality. 547-559. 1978
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On modules in which idempotent reducts form a chain.
Colloquium Mathematicum.
191-196.
1978
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On the arity of affine modules.
Colloquium Mathematicum.
1-4.
1977
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TORSION THEORIES IN AFFINE CATEGORIES.
Acta Mathematica Hungarica.
351-369.
1977
- IDEMPOTENT REDUCTS OF ABELIAN-GROUPS. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 171-182. 1976
- The operation ISKP on classes of algebras. Algebra Universalis. 349-353. 1976
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Random models of idempotent linear Maltsev conditions. I. Idemprimality.
Algebra Universalis.
2020
Teaching
courses taught
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MATH 3140 - Abstract Algebra 1
Primary Instructor - Spring 2021
Studies basic properties of algebraic structures with a heavy emphasis on groups. Other topics, time permitting, may include rings and fields. -
MATH 3170 - Combinatorics 1
Primary Instructor - Fall 2018 / Fall 2019 / Fall 2020
Covers basic methods and results in combinatorial theory. Includes enumeration methods, elementary properties of functions and relations, and graph theory. Emphasizes applications. -
MATH 3210 - Euclidean and Non-Euclidean Geometry
Primary Instructor - Spring 2020
Axiomatic systems; Euclid's presentation of the elements of geometry; Hilbert's axioms; neutral, Euclidean and non-Euclidean geometries and their models. -
MATH 4000 - Foundations of Mathematics
Primary Instructor - Fall 2018
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Same as MATH 5000. -
MATH 5000 - Foundations of Mathematics
Primary Instructor - Fall 2018
Focuses on a complete deductive framework for mathematics and applies it to various areas. Presents Goedel's famous incompleteness theorem about the inherent limitations of mathematical systems. Uses idealized computers to investigate the capabilities and limitations of human and machine computation. Department enforced prerequisites: MATH 2130 and MATH 3140. Same as MATH 4000. -
MATH 6130 - Algebra 1
Primary Instructor - Fall 2019
Studies group theory and ring theory. Department enforced prerequisite: MATH 3140. Instructor consent required for undergraduates. -
MATH 6730 - Set Theory
Primary Instructor - Spring 2019 / Spring 2021
Presents cardinal and ordinal arithmetic, and basic combinatorial concepts, including stationary sets, generalization of Ramsey's theorem, and ultrafilters, consisting of the axiom of choice and the generalized continuum hypothesis. Department enforced prerequisites: MATH 4000 or MATH 5000 and MATH 4730 or MATH 5730. Instructor consent required for undergraduates.
Background
education and training
- D.Sc., Hungarian Academy of Sciences (Hungary) 1993
- Ph.D., Hungarian Academy of Sciences (Hungary) 1982