This article is cited in 5 papers

On abelian groups with commuting monomorphisms

A. R. Chekhlov

Tomsk State University, Tomsk, Russia

Abstract: We find necessary and sufficient conditions under which an abelian group with commuting monomorphisms has the endomorphism ring normal. We describe divisible groups with left- or righ-tinvariant monomorphisms and prove that a reduced torsion-free group with left- or right-invariant monomorphisms has the endomorphism ring normal. Necessary and sufficient conditions are indicated for the left and right invariance of monomorphisms from some classes of splitting groups.

Keywords: left (right) invariance of monomorphisms, normal endomorphism ring, central idempotent endomorphism.

UDC: 512.541

Received: 04.10.2012

 English version: Siberian Mathematical Journal, 2013, 54:5, 946–950

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