On the equivalence of some sets of identities satisfied in Abelian Groups
by
Krystyna Mruczek
Institute of Mathematics, University of Opole

Let t be type of Abelian Groups. In this paper we consider the equational theories Ex(G) and Ex(Gⁿ) defined by so-called externally compatible identities of Abelian Groups and their extension. We will prove that each equational theory Cn(Ex(Gⁿ) \/ {s = s'}), where s = s' is an identity of type t, is equal to the extension of the equational theory Cn(Ex(Gⁿ) \/ E), where E is a final set of one variable identities of type t.

Date received: February 1, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagi-18.