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 | References | Similar Articles | Additional Information
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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Additional Information
Keywords:
Quasi-projective module,
projective cover,
perfect ring,
quasi-projective cover,
quasi-injective module,
semisimple ring
Article copyright:
© Copyright 1970
American Mathematical Society