Quasi-projective modules and the finite exchange property
We define a module M to be directly refinable if whenever M=A+B, there exists A¯⊆A and B¯⊆B such that M=A¯⊕B¯ . Theorem. Let M be a quasi-projective module. Then M is directly refinable if and only if M has the finite exchange property.
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1989-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171289001018 |
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| _version_ | 1850176152328470528 |
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| author | Gary F. Birkenmeier |
| author_facet | Gary F. Birkenmeier |
| author_sort | Gary F. Birkenmeier |
| collection | DOAJ |
| description | We define a module M to be directly refinable if whenever M=A+B,
there exists A¯⊆A
and B¯⊆B
such that M=A¯⊕B¯
. Theorem. Let M be a quasi-projective
module. Then M is directly refinable if and only if M has the finite
exchange property. |
| format | Article |
| id | doaj-art-b768e2fa267f476daffd9fb175037883 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1989-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b768e2fa267f476daffd9fb1750378832025-08-20T02:19:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251989-01-0112482182210.1155/S0161171289001018Quasi-projective modules and the finite exchange propertyGary F. Birkenmeier0Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USAWe define a module M to be directly refinable if whenever M=A+B, there exists A¯⊆A and B¯⊆B such that M=A¯⊕B¯ . Theorem. Let M be a quasi-projective module. Then M is directly refinable if and only if M has the finite exchange property.http://dx.doi.org/10.1155/S0161171289001018 |
| spellingShingle | Gary F. Birkenmeier Quasi-projective modules and the finite exchange property International Journal of Mathematics and Mathematical Sciences |
| title | Quasi-projective modules and the finite exchange property |
| title_full | Quasi-projective modules and the finite exchange property |
| title_fullStr | Quasi-projective modules and the finite exchange property |
| title_full_unstemmed | Quasi-projective modules and the finite exchange property |
| title_short | Quasi-projective modules and the finite exchange property |
| title_sort | quasi projective modules and the finite exchange property |
| url | http://dx.doi.org/10.1155/S0161171289001018 |
| work_keys_str_mv | AT garyfbirkenmeier quasiprojectivemodulesandthefiniteexchangeproperty |