Graded multiplication modules and the graded ideal qg (M)

Authors : Shahabaddin Ebrahimi ATANI, Reza Ebrahimi Atani

Pages : 1-9

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :Let G be a group and let R be a G-graded commutative ring. For a graded R-module M, the notion of the associated graded ideal qg insert ignore into journalissuearticles values(M); of R is defined. It is proved that the graded ideal qg insert ignore into journalissuearticles values(M); is important in the study of graded multiplication modules. Among various application given, the following results are proved: if M is a graded faithful multiplication module, then qg insert ignore into journalissuearticles values(M); is an idempotent graded multiplication ideal of R such that qg insert ignore into journalissuearticles values(qg insert ignore into journalissuearticles values(M);); = qg insert ignore into journalissuearticles values(M);, and every graded representable multiplication R-module is finitely generated.
Keywords : Graded multiplication modules, Graded ideal qg M, , Graded secondary modules