MATHEMATICS

Nil radical of the endomorphism ring of a completely decomposable torsion-free abelian group

A. V. Budanov

Tomsk State University

Abstract: Matrix ring representation of the endomorphism ring of a completely decomposable torsion-free abelian group is considered. The nil radical of such an endomorphism ring is described in terms of matrices. It is proved that the nil radical coincides with the sum of all its nilpotent ideals.

Keywords: endomorphism ring, abelian group, nil radical.

UDC: 512.541

Received: 08.11.2011