Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 46, No. 2, pp. 405-422 (2005)
Residual submodules of multiplication modules
Majid M. AliDepartment of Mathematics, Sultan Qaboos University, Muscat, Oman, e-mail: firstname.lastname@example.org
Abstract: 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
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Electronic version published on: 18 Oct 2005. This page was last modified: 29 Dec 2008.