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On modules whose endomorphism ring is local

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Abstract

The paper is a study of modules with a local endomorphism ring. We consider decompositions of modules and give a simple proof of Azumaya’s theorem. We also define an equivalence relation on the family of direct summands of a module, and show that the properties of a decomposition are closely related to the properties of this equivalence relation.

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Author notes

  1. István Beck

    Present address: Department of Mathematics, University of Bergen, 5014, Bergen, Norway

Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel

    István Beck

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  1. István Beck
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Supported by the Norwegian Research Council for Science and the Humanities.

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Beck, I. On modules whose endomorphism ring is local. Israel J. Math. 29, 393–407 (1978). https://doi.org/10.1007/BF02761177

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  • DOI: https://doi.org/10.1007/BF02761177

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