Quasivarieties and q-Compact Classes of Abelian Groups

Abstract

For the purposes of algebraic geometry, we need to consider a category of Abelian $A$-groups, that is, those Abelian groups that contain as a subgroup the distinguished copy of an Abelian group $A$. Namely, we deal with the problem of describing $q$-compact classes within a given class of algebraic systems. This problem is solved first for classes of Abelian groups (without constants), and then — for the case where a class of $A$-groups consists of the group $A$ itself. We also succeed in obtaining an adequate description of a system of axioms for $A - {\text{q}}\operatorname{var} \left( B \right)$.