Vol. 63, No. 1, 1976

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ISSN: 0030-8730
Abelian groups in which every endomorphism is a left multiplication

William Jennings Wickless

Vol. 63 (1976), No. 1, 301–307
Abstract

Let G+be an abelian group. With each multiplication on G (binary operation such that G + ∗⟩ is a ring) and each g G is associated the endomorphism gl of left multiplication by g. Let L(G) = {gl|g G,𝜖 Mult G}. Abelian groups G such that L(G) = E(G) are studied. Such groups G are characterized if G is torsion, reduced algebraically compact, completely decomposable, or almost completely decomposable of rank two. A partial results is obtained for mixed groups.

Mathematical Subject Classification 2000
Primary: 20K30
Milestones
Received: 3 October 1975
Revised: 5 November 1975
Published: 1 March 1976
Authors
William Jennings Wickless