Gamma—rings and multiplications on abelian groups

Autor:	Stefan Veldsman, A. J. M. Snyders
Rok vydání:	1992
Předmět:	Discrete mathematics Combinatorics Algebra and Number Theory Group (mathematics) G-module Elementary abelian group Cyclic group Group homomorphism Abelian group Rank of an abelian group Free abelian group Mathematics
Zdroj:	Communications in Algebra. 20:3741-3757
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927879208824539
Popis:	If M and Γ are abelian groups, then M will be a Γ-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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3839fa998e08d30eb6228bdb7fda7b79 https://doi.org/10.1080/00927879208824539 Zobrazit plný text záznamu