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Proceedings of the American Mathematical Society

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

 

 

On Zimmermann-Huisgen's splitting theorem


Author: Victor Camillo
Journal: Proc. Amer. Math. Soc. 94 (1985), 206-208
MSC: Primary 16A64; Secondary 16A30, 16A52
MathSciNet review: 784163
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Abstract: This note is motivated by a paper of Birge Zimmermann-Huisgen, which in turn is motivated by a long sequence of papers--the first due to Faith--dealing with the question of when the canonical embedding of a direct sum of modules in the corresponding direct product splits. Zimmermann-Huisgen answered a question raised by previous authors by showing that if $ R$ is a von Neumann regular ring the only way this can happen is that, except for a finite number, the modules involved must each be semisimple with only a finite number of simple modules involved.

Based on a new, more elementary argument, we establish a necessary condition for the sum-product splitting over an arbitrary (associative) ring ft (with identity).


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DOI: https://doi.org/10.1090/S0002-9939-1985-0784163-6
Article copyright: © Copyright 1985 American Mathematical Society