Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 47, No. 2, pp. 305-327 (2006)

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Multiplication Modules and Tensor Product

Majid M. Ali

Department of Mathematics, Sultan Qaboos University, Muscat, Oman, e-mail: mali@squ.edu.om

Abstract: All rings are commutative with identity and all modules are unital. The tensor product of projective (resp. flat, multiplication) modules is a projective (resp. flat, multiplication) module but not conversely. In this paper we give some conditions under which the converse is true. We also give necessary and sufficient conditions for the tensor product of faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) modules to be a faithful multiplication Dedekind (resp. Prüfer, finitely cogenerated, uniform) module. Necessary and sufficient conditions for the tensor product of pure (resp. invertible, large, small, join principal) submodules of multiplication modules to be a pure (resp. invertible, large, small, join principal) submodule are also considered.

Keywords: Multiplication module, projective module, flat module, cancellation module, pure submodule, invertible submodule, large submodule, small submodule, join principal submodule, tensor product

Classification (MSC2000): 13C13, 13A15, 15A69

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Electronic version published on: 19 Jan 2007. This page was last modified: 5 Nov 2009.

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