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Informatics Report Series
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| Title:On Isolated Submodules |
| Authors:
Roy McCasland
; Patrick F. Smith
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| Date:Aug 2006 |
| Publication Title:Communications in Algebra |
| Publisher:Taylor & Francis |
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Publication Type:Journal Article
Publication Status:Published
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Volume No:34(8)
Page Nos:2977-2988
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DOI:10.1080/00927870600639773
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- Abstract:
- Let R be a ring with identity and let M be a unital left R-module. A proper submodule L of M is radical if L is an intersection of prime submodules of M. Moreover, a submodule L of M is isolated if, for each proper submodule N of L, there exists a prime submodule K of M such that N is contained in K but L is not contained in K. It is proved that every proper submodule of M is radical (and hence every submodule of M is isolated) if and only if N intersected with IM is equal to IN for every submodule N of M and every (left primitive) ideal I of R. In case, R/P is an Artinian ring for every left primitive ideal P of R it is proved that a finitely generated submodule N of a non-zero left R-module M is isolated if and only if PN equals N intersect PM for every left primitive ideal P of R. If R is a commutative ring then a finitely generated submodule N of a projective R-module M is isolated if and only if N is a direct summand of M.
- Links To Paper
- Link to listing (subscription required)
- Bibtex format
- @Article{EDI-INF-RR-0591,
- author = {
Roy McCasland
and Patrick F. Smith
},
- title = {On Isolated Submodules},
- journal = {Communications in Algebra},
- publisher = {Taylor & Francis},
- year = 2006,
- month = {Aug},
- volume = {34(8)},
- pages = {2977-2988},
- doi = {10.1080/00927870600639773},
- url = {http://taylorandfrancis.metapress.com/openurl.asp?genre=article&eissn=1532-4125&volume=34&issue=8&spage=2977},
- }
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