Equational co-domains in the class of abelian groups (paper dedicated to professor Vladimir Nikanorovich Remeslennikov on the occasion of his 80th birthday)
Equational co-domains are determined by the property that above them all non-empty algebraic sets are irreducible. The description of equational co-domains in the class of abelian groups is given in this article. It is proved that the property of “being an equational co-domain” for an abelian group does not depend on the presence or absence of non-zero coefficients in the used equations. It is shown that the class of equational co-domains in the variety of abelian groups is axiomatizable. The corresponding list of axioms is given.