Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 46, No. 2, pp. 405-422 (2005)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 405-422 (2005) |
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Residual submodules of multiplication modulesMajid M. AliDepartment of Mathematics, Sultan Qaboos University, Muscat, Oman, e-mail: mali@squ.edu.omAbstract: Let $R$ be a commutative ring with identity and $M$ an $R$-module. We introduce and give some properties and characterizations of the concepts of $M$-cancellation, $M$-weak cancellation, $M$-meet principal, and $M$-weak meet principal ideals. We prove that a submodule of a faithful multiplication module is faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) if and only if its residual by a finitely generated faithful multiplication ideal is a faithful (resp. finitely generated, multiplication, flat, projective, pure, prime) submodule. Keywords: multiplication module, residual submodule, cancellation ideal, meet-principal ideal Classification (MSC2000): 13C13, 13C05, 13A15 Full text of the article:
Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.
© 2005 Heldermann Verlag
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