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On Zimmermann-Huisgen's Splitting Theorem
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On Zimmermann-Huisgen's Splitting Theorem

Victor Camillo
Proceedings of the American Mathematical Society, Vol.94(2), pp.206-208
06/1985
DOI: 10.2307/2045375

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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 R (with identity).

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