MATHEMATICS

Quasi-noninvertible endomorphisms of abelian groups

A. V. Budanov

Tomsk State University, Faculty of Mechanics and Mathematics

Abstract: We define and study quasi-noninvertible endomorphisms of torsion-free abelian groups. For completely decomposable and separable groups a description of quasi-noninvertible endomorphisms is provided in terms of their action on direct summands of rank 1. For these classes of groups we study the structure of the factor ring of the endomorphism ring modulo the ideal of all quasi-noninvertible endomorphisms and the connection between this ideal and the nil radical.

Keywords: abelian group, endomorphism ring.

UDC: 512.552


Accepted: June 10, 2010