Gamma-rings and multiplications on abelian groups

A. J M Snyders, S. Veldsman

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Abstract

If M and Γ are abelian groups, then M will be a T—ring iff there exists a group homomorphism f from Γ into the group of all multiplications of M, Mult(M), such that f(Γ) satisfies the Generalized Associativity Property on M. In this note we examine the following special cases of this result: (i) M is a Γ—ring satisfying the Nobusawa Condition, (ii) M is a cyclic group, (iii) M is a direct sum of cyclic groups and (iv) M is a Γ-ring that has unity elements.

Original languageEnglish
Pages (from-to)3741-3757
Number of pages17
JournalCommunications in Algebra
Volume20
Issue number12
DOIs
Publication statusPublished - Jan 1 1992

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ASJC Scopus subject areas

  • Algebra and Number Theory

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