Semi-perfect and F-semi-perfect modules

A module is semi-perfect iff every factor module has a projective cover. A module M=A+B (for submodules A and B) is amply supplemented iff there exists a submodule A′ (called a supplement of A) of B such M=A+A′ and A′ is minimal with this property. If B=M then M is supplemented. Kasch and Mares [1]...

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Bibliographic Details
Published in:International Journal of Mathematics and Mathematical Sciences
Main Author: David J. Fieldhouse
Format: Article
Language:English
Published: Wiley 1985-01-01
Subjects:
F-semi-perfect module
projective cover
semi-perfect module
small submodule
supplement.
Online Access:http://dx.doi.org/10.1155/S0161171285000588
Description
Summary:A module is semi-perfect iff every factor module has a projective cover. A module M=A+B (for submodules A and B) is amply supplemented iff there exists a submodule A′ (called a supplement of A) of B such M=A+A′ and A′ is minimal with this property. If B=M then M is supplemented. Kasch and Mares [1] have shown that the first and last of these conditions are equivalent for projective modules. Here it is shown that an arbitrary module is semi-perfect iff it is (amply) supplemented by supplements which have projective covers, an extension of the result of Kasch and Mares [1]. Corresponding results are obtained for F-semi-perfect modules.
ISSN:0161-1712
1687-0425

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