Finite simple zeropotent paramedial groupoids

The Equational Theory of Paramedial Cancellation Groupoids

By a paramedial groupoid we mean a groupoid satisfying the equation xy · zu = uy · zx. As it is easy to see, the equational theory of paramedial groupoids, as well as the equational theory based on any balanced equation, is decidable. In this paper we are going to investigate the equational theory of paramedial cancellation groupoids; by this we mean the set of all equations satisfied by parame...

Finite Groupoids, Finite Coverings and Symmetries in Finite Structures

We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual sense, but with respect to a discounted distance measure that contracts arbitrarily long sequences of edges within the same sub-groupoid (coset) and only co...

Finite embeddability property for residuated groupoids

A very simple proof of the finite embeddability property for residuated distributivelattice-ordered groupoids and some related classes of algebras is presented. In particular, this gives an answer to the question posed in [3, Problem 4.2]. The presented construction allows for improvement of the upper bound on the complexity of the decision procedure for the universal theory of residuated distr...

Finite idempotent groupoids and regular languages

Membership Problems for Finite Entropic Groupoids

Some abstract here.