Invertibility of Multiplication Modules III


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New Zealand Journal of Mathematics

Vol. 39, (2009), Pages 193-213

Majid M. Ali

Department of Mathematics and Statistics

Sultan Qaboos University

Muscat, Oman

Abstract All rings are commutative with identity and all modules are unital. We introduce and investigate the concepts of generalized Dedekind modules and almost Dedekind modules. We also characterize faithful multiplication valuation modules via m-canonical submodules. Finally, we give some properties of a lattice of submodules of a faithful multiplication Prufer module.

Keywords multiplication module, Dedekind module, valuation module, Prufer module, $m$-canonical submodule.

Classification (MSC2000) Primary: 3C13, 13A15.

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