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On some sets of identities satisfied in Abelian groups

Gajewska-Kurdziel K., Mruczek K.

Demonstratio Mathematica

2002

Vol. 35, nr 3

447-453

The equational theories were studied in many works (see [4], [5], [6], [7]). Let T be a type of Abelian groups. In this paper we consider the extentions of the equational theory Ex(Gn) defined by so called externally compatible identities of Abelian groups and the identity xn = yn. The equational base of this theory was found in [3]. We prove that each equational theory Cn(Ex^(Gn) U {(phi=epsilon}), where phi=epsilon is an identity of type r, is equal to the extension of the equational theory Cn{Ex{Gn) U E), where E is a finite set of one variable identities of type r. The notation in this paper are the same as in [1].