28 citations · 57 across the 10 of their papers we have counts for
16 papers
Abelianness and centrality in inverse semigroups
Michael Kinyon, David Stanovský
We adapt the abstract concepts of abelianness and centrality of universal algebra to the context of inverse semigroups. We characterize abelian and central congruences in terms of…
Supernilpotent groups and -supernilpotent loops
David Stanovský, Petr Vojtěchovský
We find a short equational basis for the variety of -supernilpotent loops. We also present a conceptually simple proof that -nilpotence and -supernilpotence are equivalent…
Three concepts of nilpotence in loops
Žaneta Semanišinová, David Stanovský
We introduce the abstract concept of supernilpotence in loop theory, and relate it to existing concepts, namely, central nilpotence and nilpotence of the multiplication group. We p…
Homomorphic images of affine quandles
Přemysl Jedlička, David Stanovský
We are interested in abstract conditions that characterize homomorphic images of affine quandles. Our main result is a two-fold characterization of this class: one by a property of…
Idempotent solutions of the Yang-Baxter equation and twisted group division
David Stanovský, Petr Vojtěchovský
Idempotent left nondegenerate solutions of the Yang-Baxter equation are in one-to-one correspondence with twisted Ward left quasigroups, which are left quasigroups satisfying the i…
Involutive latin solutions of the Yang-Baxter equation
Marco Bonatto, Michael Kinyon, David Stanovský +1
Wolfgang Rump showed that there is a one-to-one correspondence between nondegenerate involutive set-theoretic solutions of the Yang-Baxter equation and binary algebras in which all…
A Universal algebraic approach to rack coverings
Marco Bonatto, David Stanovský
We study rack and quandle coverings from a universal algebraic viewpoint and we show how they can be understood using the notion of strongly abelian congruences. We provide an abst…
Commutator theory for racks and quandles
Marco Bonatto, David Stanovský
We adapt the commutator theory of universal algebra to the particular setting of racks and quandles, exploiting a Galois connection between congruences and certain normal subgroups…
Subquandles of affine quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
A quandle will be called quasi-affine, if it embeds into an affine quandle. Our main result is a characterization of quasi-affine quandles, by group-theoretic properties of their d…
Medial quasigroups of prime square order
David Stanovský
We prove that, for any prime , there are precisely medial quasigroups of order , up to isomorphism.
Central and medial quasigroups of small order
David Stanovský, Petr Vojtěchovský
We enumerate central and medial quasigroups of order less than up to isomorphism, with the exception of those quasigroups that are isotopic to , , $C_…
Commutator theory for loops
David Stanovský, Petr Vojtěchovský
Using the Freese-McKenzie commutator theory for congruence modular varieties as the starting point, we develop commutator theory for the variety of loops. The fundamental theorem o…
The origins of involutory quandles
David Stanovský
We present an overview of some older papers on involutory quandles, mostly from the times before the term "quandle" was born. It is meant as a reference guide, not (yet) as an expo…
A guide to self-distributive quasigroups, or latin quandles
David Stanovský
We present an overview of the theory of self-distributive quasigroups, both in the two-sided and one-sided cases, and relate the older results to the modern theory of quandles, to…
The structure of medial quandles
Přemysl Jedlička, Agata Pilitowska, David Stanovský +1
Medial quandles are represented using a heterogeneous affine structure. As a consequence, we obtain numerous structural properties, including enumeration of isomorphism classes of…
Connected quandles and transitive groups
Alexander Hulpke, David Stanovský, Petr Vojtěchovský
We establish a canonical correspondence between connected quandles and certain configurations in transitive groups, called quandle envelopes. This correspondence allows us to effic…