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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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000588 |
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| _version_ | 1832559869214851072 |
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| author | David J. Fieldhouse |
| author_facet | David J. Fieldhouse |
| author_sort | David J. Fieldhouse |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-e406dec631364da398b3571de63d1cb4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-e406dec631364da398b3571de63d1cb42025-02-03T01:29:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-018354554810.1155/S0161171285000588Semi-perfect and F-semi-perfect modulesDavid J. Fieldhouse0Department of Mathematics and Statistics, University of Guelph, Guelph N1G 2W1, Ontario, CanadaA 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.http://dx.doi.org/10.1155/S0161171285000588F-semi-perfect moduleprojective coversemi-perfect modulesmall submodulesupplement. |
| spellingShingle | David J. Fieldhouse Semi-perfect and F-semi-perfect modules International Journal of Mathematics and Mathematical Sciences F-semi-perfect module projective cover semi-perfect module small submodule supplement. |
| title | Semi-perfect and F-semi-perfect modules |
| title_full | Semi-perfect and F-semi-perfect modules |
| title_fullStr | Semi-perfect and F-semi-perfect modules |
| title_full_unstemmed | Semi-perfect and F-semi-perfect modules |
| title_short | Semi-perfect and F-semi-perfect modules |
| title_sort | semi perfect and f semi perfect modules |
| topic | F-semi-perfect module projective cover semi-perfect module small submodule supplement. |
| url | http://dx.doi.org/10.1155/S0161171285000588 |
| work_keys_str_mv | AT davidjfieldhouse semiperfectandfsemiperfectmodules |