-Regular Modules

Areej M. Abduldaim and Sheng Chen

Journal of Applied Mathematics, 2013, vol. 2013, 1-7

Abstract:

We introduced and studied -regular modules as a generalization of -regular rings to modules as well as regular modules (in the sense of Fieldhouse). An -module is called -regular if for each and , there exist and a positive integer such that . The notion of -pure submodules was introduced to generalize pure submodules and proved that an -module is -regular if and only if every submodule of is -pure iff is a -regular -module for each maximal ideal of . Many characterizations and properties of -regular modules were given. An -module is -regular iff is a -regular ring for each iff is a -regular ring for finitely generated module . If is a -regular module, then .

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:630285

DOI: 10.1155/2013/630285

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