Gamma-rings and multiplications on abelian groups

A. J M Snyders; S. Veldsman

doi:10.1080/00927879208824539

Gamma-rings and multiplications on abelian groups

A. J M Snyders, S. Veldsman

Mathematics & Statistics

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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 language	English
Pages (from-to)	3741-3757
Number of pages	17
Journal	Communications in Algebra
Volume	20
Issue number	12
DOIs	https://doi.org/10.1080/00927879208824539
Publication status	Published - Jan 1 1992

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ASJC Scopus subject areas

Algebra and Number Theory

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Snyders, A. J. M., & Veldsman, S. (1992). Gamma-rings and multiplications on abelian groups. Communications in Algebra, 20(12), 3741-3757. https://doi.org/10.1080/00927879208824539

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10.1080/00927879208824539