Commutator theory for relatively modular quasivarieties

Abstract

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.