On free expansions and algorithmic problems in $R$-varieties of universal algebras

A class of varieties of universal algebras is pointed out (and described by systems of quasi-identities) in which the algorithmic problems of word identity, isomorphism, and occurrence are definitely decidable and in which, as well, theorems on free algebras and free products of algebras hold which are analogous to the theorems of Nielsen–Schreier and Kurosh and certain corollaries of Grushko's grouptheoretic theorem.
Bibliography: 17 titles.