On elementarily of radical classes of modules over noncommutative dedekind duo-domains

Abstract

We find some sufficient conditions for a radical class of an idempotent radical in the category of modules over a Dedekind left bounded duo-domain to be axiomatisable. In the case of the integer numbers ring this result implies the Gorbachuk-Komarnitskii Theorem on axiomatizable radical classes of abelian groups.