Principal and Syntactic Congruences in Congruence-Distributive and Congruence-Permutable Varieties

Abstract

We give a new proof that a finitely generated congruence-distributive variety has finitely determined syntactic congruences (or, equivalently, term finite principal congruences), and show that the same does not hold for finitely generated congruence-permutable varieties, even under the additional assumption that the variety is residually very finite.2000 Mathematics subject classification: 08B10.

Internet Security Applications of Gröbner-Shirshov Bases

“…Let us refer, for example, to [13,14,16,18,19,21] for examples of recent related results. Suppose that S = M 0 (G; I, Λ; P ) is a Rees matrix semigroup and T is a subsemigroup in S. Denote by L = L(T ) the set…”

“…Let us include a few references to articles using constructions of this sort [11,12,15,16,25,28,[30][31][32][33][34][35].…”

Optimal Rees Matrix Constructions for Analysis of Data

“…Rees matrix semigroups and the associated notions of completely 0-simple semigroups and Rees quotients are well known in semigroup theory and play crucial roles in describing the structure of semigroups and in proofs; see [9]. For examples of recent results, we also refer to [4,[10][11][12].…”

Rees Matrix Constructions for Clustering of Data

“…The present paper uses contracted semigroup rings, which helps to record our results more concisely. These constructions are used and considered, for example, in [1,9,11,12,14,16,32].…”