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Jónsson and HS Modules over Commutative Rings

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  • Greg Oman

Abstract

Let be a commutative ring with identity and let be an infinite unitary -module. (Unless indicated otherwise, all rings are commutative with identity 1 ≠ 0 and all modules are unitary.) Then is called a Jónsson module provided every proper submodule of has smaller cardinality than . Dually, is said to be homomorphically smaller (HS for short) if for every nonzero submodule of . 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.

Suggested Citation

  • Greg Oman, 2014. "Jónsson and HS Modules over Commutative Rings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-13, March.
    • Handle: RePEc:hin:jijmms:120907
    DOI: 10.1155/2014/120907
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