Invertibility of Multiplication Modules IV

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New Zealand Journal of Mathematics

Vol. 43, (2013), Pages 65-84


Majid M. Ali

Department of Mathematics and Statistics

Sultan Qaboos University

P.O. Box 36, PC. 123 Alkhoud

Muscat,

Sultanate of Oman mailto:mali@squ.edu.om






Abstract All rings are commutative with identity and all modules are unital. We give several properties of quasi-invertible submodules of multiplication modules generalizing those of quasi-invertible ideals. We introduce the concepts of generalized Dedekind modules, completely integrally closed modules, * -modules and v-multiplication modules and study the relationship among these modules in case they are faithful multiplication modules over integral domains. Finally, we introduce RTP and TPP modules and show that they are equivalent in the class of one dimensional faithful multiplication modules.

Keywords multiplication module, v-submodule, quasi-invertible submodule, generalized Dedekind module, completely integrally closed module, *-module, RTP and TPP modules.

Classification (MSC2000) 13C13, 13A15.

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