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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171285000588 |
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| 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. |
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| ISSN: | 0161-1712 1687-0425 |