We develop a commutator theory for relatively modular quasivarieties that extends the theory for modular varieties. We characterize relatively modular quasivarieties, prove that they have an almost-equational axiomatization and we investigate the lattice of subquasivarieties. We derive the result that every finitely generated, relatively modular quasivariety of semigroups is finitely based.

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

We provide explicit constructions for various ingredients of right exact monoidal structures on the category finitely presented functors. As our main tool, we prove a multilinear version universal property so-called Freyd categories, which in turn is used proof correctness constructions. Furthermore, compare construction with Day convolution arbitrary additive always yields closed structure all...

We show that the equational theory of representable lattice-ordered residuated semigroups is not finitely axiomatizable. We apply this result to the problem of completeness of substructural logics.

A variety of semigroups that is minimal with respect to being non-finitely based is said to be a limit variety. By Zorn’s Lemma, each non-finitely based variety contains at least one limit subvariety. Although many examples of non-finitely based varieties are known in the literature (see [3, 5]), explicit examples of limit varieties are very rarely discovered [1, 2, 4]. The objective of the pre...