Ágnes Szendrei
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Ágnes Szendrei has a total of 6 co-authors. Here are the top co-authors by number of shared publications:
- Keith A. Kearnes
Department of Mathematics, University of Colorado, Boulder, USA
12 shared publications - Emil W. Kiss
Department of Algebra and Number Theory, Loránd Eötvös University, Budapest, Hungary
6 shared publications - Peter Mayr
Department of Mathematics, University of Colorado, Boulder, USA
2 shared publications - Ross Willard
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
2 shared publications - Pham Ngoc Ánh
Hungarian Academy of Sciences
1 shared publication - Topaz Dent
University of Colorado
1 shared publication
Latest Publications
- 7 September 2021
- Published by Springer Nature in Algebra universalis
- Vol. 82 (4) , 1-39
Algebras from congruences
- 7 September 2021
- Published by Springer Nature in Algebra universalis
- Vol. 82 (4) , 1-39
Algebras from congruences
- Open Access
Algebras from Congruences
We present a functorial construction which, starting from a congruence $\alpha$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences between 0 and $\alpha$ on A, this isomorphism preserves higher commutators and TCT types, and C inherits all idempotent Maltsev conditions from A. As applications of this construction, we first show that supernilpotence is decidable for congruences of finite algebras in varieties that omit type 1. Secondly, we prove that the subpower membership problem for finite algebras with a cube term can be effectively reduced to membership questions in subdirect products of subdirectly irreducible algebras with central monoliths. As a consequence, we obtain a polynomial time algorithm for the subpower membership problem for finite algebras with a cube term in which the monolith of every subdirectly irreducible section has a supernilpotent centralizer.Open AccessAlgebras from Congruences
We present a functorial construction which, starting from a congruence $\alpha$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences between 0 and $\alpha$ on A, this isomorphism preserves higher commutators and TCT types, and C inherits all idempotent Maltsev conditions from A. As applications of this construction, we first show that supernilpotence is decidable for congruences of finite algebras in varieties that omit type 1. Secondly, we prove that the subpower membership problem for finite algebras with a cube term can be effectively reduced to membership questions in subdirect products of subdirectly irreducible algebras with central monoliths. As a consequence, we obtain a polynomial time algorithm for the subpower membership problem for finite algebras with a cube term in which the monolith of every subdirectly irreducible section has a supernilpotent centralizer. - 3 June 2020
- Published by Springer Nature
- p. 1-9
Commutative Rings Whose Principal Ideals Have Unique Generators
- 3 June 2020
- Published by Springer Nature
- p. 1-9
Commutative Rings Whose Principal Ideals Have Unique Generators
- 5 March 2018
- Published by Springer Nature in Algebra universalis
- Vol. 79 (1) , 3
Varieties whose finitely generated members are free
- 5 March 2018
- Published by Springer Nature in Algebra universalis
- Vol. 79 (1) , 3
Varieties whose finitely generated members are free
- 6 November 2017
- Published by Springer Nature in Algebra universalis
- Vol. 78 (4) , 555-561
Simpler Maltsev conditions for (weak) difference terms in locally finite varieties
- 6 November 2017
- Published by Springer Nature in Algebra universalis
- Vol. 78 (4) , 555-561
Simpler Maltsev conditions for (weak) difference terms in locally finite varieties
- Open Access
Varieties whose finitely generated members are free
We prove that a variety of algebras whose finitely generated members are free must be definitionally equivalent to the variety of sets, the variety of pointed sets, a variety of vector spaces over a division ring, or a variety of affine vector spaces over a division ring.
Open AccessVarieties whose finitely generated members are free
We prove that a variety of algebras whose finitely generated members are free must be definitionally equivalent to the variety of sets, the variety of pointed sets, a variety of vector spaces over a division ring, or a variety of affine vector spaces over a division ring.
- Open Access
Cube term blockers without finiteness
We show that an idempotent variety has a $d$-dimensional cube term if and only if its free algebra on two generators has no $d$-ary compatible cross. We employ Hall's Marriage Theorem to show that a variety of finite signature whose fundamental operations have arities $n_1, \ldots, n_k$ has a $d$-dimensional cube term if and only if it has one of dimension $d=1+\sum_{i=1}^k (n_i-1)$. This lower bound on dimension is shown to be sharp. We show that a pure cyclic term variety has a cube term if and only if it contains no $2$-element semilattice. We prove that the Maltsev condition "existence of a cube term" is join prime in the lattice of idempotent Maltsev conditions.Open AccessCube term blockers without finiteness
We show that an idempotent variety has a $d$-dimensional cube term if and only if its free algebra on two generators has no $d$-ary compatible cross. We employ Hall's Marriage Theorem to show that a variety of finite signature whose fundamental operations have arities $n_1, \ldots, n_k$ has a $d$-dimensional cube term if and only if it has one of dimension $d=1+\sum_{i=1}^k (n_i-1)$. This lower bound on dimension is shown to be sharp. We show that a pure cyclic term variety has a cube term if and only if it contains no $2$-element semilattice. We prove that the Maltsev condition "existence of a cube term" is join prime in the lattice of idempotent Maltsev conditions. - 22 January 2016
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 101 (1) , 56-94
GROWTH RATES OF ALGEBRAS, I: POINTED CUBE TERMS
We investigate the function $d_{\mathbf{A}}(n)$ , which gives the size of a least size generating set for $\mathbf{A}^{n}$ .- 22 January 2016
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 101 (1) , 56-94
GROWTH RATES OF ALGEBRAS, I: POINTED CUBE TERMS
We investigate the function $d_{\mathbf{A}}(n)$ , which gives the size of a least size generating set for $\mathbf{A}^{n}$ .- Open Access
Dualizable algebras with parallelogram terms
We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but more importantly proves that every finite module, group or ring in a residually small variety is dualizable.
Open AccessDualizable algebras with parallelogram terms
We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but more importantly proves that every finite module, group or ring in a residually small variety is dualizable.
- Open Access
- 10 July 2015
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 368 (3) , 2115-2143
A finite basis theorem for difference-term varieties with a finite residual bound
We prove that if V \mathcal V is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, V \mathcal V has a difference term, and V \mathcal V has a finite residual bound, then V \mathcal V is finitely axiomatizable. This provides a common generalization of R. McKenzie’s finite basis theorem for congruence modular varieties with a finite residual bound, and R. Willard’s finite basis theorem for congruence meet-semidistributive varieties with a finite residual bound.
- 10 July 2015
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 368 (3) , 2115-2143
Open AccessA finite basis theorem for difference-term varieties with a finite residual bound
We prove that if V \mathcal V is a variety of algebras (i.e., an equationally axiomatizable class of algebraic structures) in a finite language, V \mathcal V has a difference term, and V \mathcal V has a finite residual bound, then V \mathcal V is finitely axiomatizable. This provides a common generalization of R. McKenzie’s finite basis theorem for congruence modular varieties with a finite residual bound, and R. Willard’s finite basis theorem for congruence meet-semidistributive varieties with a finite residual bound.