Jónsson and HS Modules over Commutative Rings
Let R be a commutative ring with identity and let M be an infinite unitary R-module. (Unless indicated otherwise, all rings are commutative with identity 1≠0 and all modules are unitary.) Then M is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. Dually, M...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/120907 |
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| _version_ | 1850110466872836096 |
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| author | Greg Oman |
| author_facet | Greg Oman |
| author_sort | Greg Oman |
| collection | DOAJ |
| description | Let R be a commutative ring with identity and let M be an infinite unitary R-module. (Unless indicated otherwise, all rings are commutative with identity 1≠0 and all modules are unitary.) Then M is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. Dually, M is said to be homomorphically smaller (HS for short) if |M/N|<|M| for every nonzero submodule N of M. In this survey paper, we bring the reader up to speed on current research on these structures by presenting the principal results on Jónsson and HS modules. We conclude the paper with several open problems. |
| format | Article |
| id | doaj-art-46b4c64d5e6a4722807da2bd0f1c6244 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-46b4c64d5e6a4722807da2bd0f1c62442025-08-20T02:37:49ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/120907120907Jónsson and HS Modules over Commutative RingsGreg Oman0Department of Mathematics, The University of Colorado, Colorado Springs, CO 80918, USALet R be a commutative ring with identity and let M be an infinite unitary R-module. (Unless indicated otherwise, all rings are commutative with identity 1≠0 and all modules are unitary.) Then M is called a Jónsson module provided every proper submodule of M has smaller cardinality than M. Dually, M is said to be homomorphically smaller (HS for short) if |M/N|<|M| for every nonzero submodule N of M. In this survey paper, we bring the reader up to speed on current research on these structures by presenting the principal results on Jónsson and HS modules. We conclude the paper with several open problems.http://dx.doi.org/10.1155/2014/120907 |
| spellingShingle | Greg Oman Jónsson and HS Modules over Commutative Rings International Journal of Mathematics and Mathematical Sciences |
| title | Jónsson and HS Modules over Commutative Rings |
| title_full | Jónsson and HS Modules over Commutative Rings |
| title_fullStr | Jónsson and HS Modules over Commutative Rings |
| title_full_unstemmed | Jónsson and HS Modules over Commutative Rings |
| title_short | Jónsson and HS Modules over Commutative Rings |
| title_sort | jonsson and hs modules over commutative rings |
| url | http://dx.doi.org/10.1155/2014/120907 |
| work_keys_str_mv | AT gregoman jonssonandhsmodulesovercommutativerings |