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Proceedings of the American Mathematical Society

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

 

 

Quasi-projective covers and direct sums


Author: Anne Koehler
Journal: Proc. Amer. Math. Soc. 24 (1970), 655-658
MSC: Primary 16.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0255596-0
MathSciNet review: 0255596
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Abstract: In this paper $ R$ denotes an associative ring with an identity, and all modules are unital left $ R$-modules. It is shown that the existence of a quasi-projective cover for each module implies that each module has a projective cover. By a similar technique the following statements are shown to be equivalent: 1. $ R$ is semisimple and Artinian; 2. Every finitely generated module is quasi-projective; and 3. The direct sum of every pair of quasi-projective modules is quasi-projective. Direct sums of quasi-injective modules are also investigated.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0255596-0
Keywords: Quasi-projective module, projective cover, perfect ring, quasi-projective cover, quasi-injective module, semisimple ring
Article copyright: © Copyright 1970 American Mathematical Society