Jónsson and HS Modules over Commutative Rings
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-03-12
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Oman, Greg. 2014. Jónsson and HS Modules over Commutative Rings. International Journal of Mathematics and Mathematical Sciences،Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-447284
Modern Language Association (MLA)
Oman, Greg. Jónsson and HS Modules over Commutative Rings. International Journal of Mathematics and Mathematical Sciences No. 2014 (2014), pp.1-13.
https://search.emarefa.net/detail/BIM-447284
American Medical Association (AMA)
Oman, Greg. Jónsson and HS Modules over Commutative Rings. International Journal of Mathematics and Mathematical Sciences. 2014. Vol. 2014, no. 2014, pp.1-13.
https://search.emarefa.net/detail/BIM-447284
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-447284