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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On rings for which homogeneous maps are linear


Authors: P. Fuchs, C. J. Maxson and G. Pilz
Journal: Proc. Amer. Math. Soc. 112 (1991), 1-7
MSC: Primary 16S50; Secondary 16Y30
DOI: https://doi.org/10.1090/S0002-9939-1991-1042265-6
MathSciNet review: 1042265
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Abstract: Let $ R$ be the collection of all rings $ R$ such that for every $ R$-module $ G$, the centralizer near-ring $ {M_R}(G) = \{ f:G \to G\vert f(rx) = rf(x),r \in R,x \in G\} $ is a ring. We show $ R \in R$ if and only if $ {M_R}(G) = {\text{En}}{{\text{d}}_R}(G)$ for each $ R$-module $ G$. Further information about $ R$ is collected and the Artinian rings in $ R$ are completely characterized.


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DOI: https://doi.org/10.1090/S0002-9939-1991-1042265-6
Article copyright: © Copyright 1991 American Mathematical Society

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