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On Direct Sums of Injective Modules and Chain Conditions

Published online by Cambridge University Press:  20 November 2018

Stanley S. Page  and
Yiqiang Zhou
Stanley S. Page
Affiliation:
Mathematics Department The University of British Columbia Vancouver, British Columbia V6T1Z2
Yiqiang Zhou
Affiliation:
Mathematics Department The University of British Columbia Vancouver, British Columbia V6T1Z2
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Abstract

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Let R be a ring and M a right R-module. Let σ[M] be the full subcategory of Mod-R subgenerated by M. An M-natural class 𝒦 is a subclass of σ[M] closed under submodules, direct sums, isomorphic copies, and M-injective hulls. We present some equivalent conditions each of which describes when σ has the property that direct sums of (M-)injective modules in σ are (M-)injective. Specializing to particular M, and/or special subclasses we obtain many new results and known results as corollaries.

Keywords

16D5016D7016P7016D7016P40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 3 , 01 June 1994 , pp. 634 - 647
Copyright
Copyright © Canadian Mathematical Society 1994

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