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1975•Transactions of the American Mathematical SocietyRequires access

Endomorphism Rings and Direct Sums of Torsion Free Abelian Groups

D. M. Arnold, E.L Lady

Open publisher page 31 citations

Abstract

Properties of abelian groups related to a given finite rank torsion free abelian group A are analyzed in terms of End (A), the endomorphism ring of A. This point of view gives rise to generalizations of some classical theorems by R. Baer and examples of pathological direct sum decompositions of finite rank torsion free abelian groups.

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Properties of abelian groups related to a given finite rank torsion free abelian group A are analyzed in terms of End (A), the endomorphism ring of A. This point of view gives rise to generalizations of some classical theorems by R. Baer and examples of pathological direct sum decompositions of finite rank torsion free abelian groups.

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Available abstract

Properties of abelian groups related to a given finite rank torsion free abelian group A are analyzed in terms of End (A), the endomorphism ring of A. This point of view gives rise to generalizations of some classical theorems by R. Baer and examples of pathological direct sum decompositions of finite rank torsion free abelian groups.

Key concepts: Mathematics, Rank of an abelian group, Abelian group, Endomorphism ring, Torsion subgroup, Elementary abelian group, Torsion (gastropod), Endomorphism

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