366 citations · 2.5k across the 44 of their papers we have counts for
9 papers · 1 filter
Clonoids between modules
Peter Mayr, Patrick Wynne
Clonoids are sets of finitary functions from an algebra to an algebra that are closed under composition with term functions of on the domain…
Vaughan--Lee's nilpotent loop of size is finitely based
Peter Mayr
In 1983 Vaughan--Lee showed that if a finite nilpotent loop splits into a direct product of factors of prime power order, then its equational theory has a finite basis. Whether the…
Generating subdirect products
Peter Mayr, Nik Ruskuc
We study conditions under which subdirect products of various types of algebraic structures are finitely generated or finitely presented. In the case of two factors, we prove gener…
Presentations for subrings and subalgebras of finite co-rank
Peter Mayr, Nik Ruskuc
Let be a commutative Noetherian ring with identity, let be a -algebra, and let be a subalgebra of such that is finitely generated as a -module. The main…
Finiteness properties of direct products of algebraic structures
Peter Mayr, Nik Ruskuc
We consider the preservation of properties of being finitely generated, being finitely presented and being residually finite under direct products in the context of different types…
Independence of algebras with edge term
Erhard Aichinger, Peter Mayr
Two varieties of the same type are independent if there is a binary term such that and . In this note, we g…
Finitely generated equational classes
Erhard Aichinger, Peter Mayr
Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that ho…
Supernilpotence prevents dualizability
Wolfram Bentz, Peter Mayr
We address the question of the dualizability of nilpotent Mal'cev algebras, showing that nilpotent finite Mal'cev algebras with a non-abelian supernilpotent congruence are inherent…
On the number of finite algebraic structures
Erhard Aichinger, Peter Mayr, Ralph McKenzie
We prove that every clone of operations on a finite set A, if it contains a Malcev operation, is finitely related -- i.e., identical with the clone of all operations respecting R f…