Journal article
On Zimmermann-Huisgen's Splitting Theorem
Proceedings of the American Mathematical Society, Vol.94(2), pp.206-208
06/1985
DOI: 10.2307/2045375
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).
Details
- Title: Subtitle
- On Zimmermann-Huisgen's Splitting Theorem
- Creators
- Victor Camillo
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.94(2), pp.206-208
- DOI
- 10.2307/2045375
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Language
- English
- Date published
- 06/1985
- Academic Unit
- Mathematics
- Record Identifier
- 9983985953502771
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