Abelian groups in which every endomorphism is a left multiplication

William Jennings Wickless

Vol. 63 (1976), No. 1, 301–307

DOI: 10.2140/pjm.1976.63.301

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 g_l^∗ of left multiplication by g. Let L(G) = {g_l^∗|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