Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 46, No. 2, pp. 405422 (2005) 

Residual submodules of multiplication modulesMajid M. AliDepartment of Mathematics, Sultan Qaboos University, Muscat, Oman, email: 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, meetprincipal 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.
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