- Turkish Journal of Mathematics
- Vol: 35 Issue: 1
- Graded multiplication modules and the graded ideal qg (M)
Graded multiplication modules and the graded ideal qg (M)
Authors : Shahabaddin Ebrahimi Atani, Reza Ebrahimi Atani
Pages : 1-9
View : 10 | Download : 7
Publication Date : 9999-12-31
Article Type : Makaleler
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 (M) of R is defined. It is proved that the graded ideal qg (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 (M) is an idempotent graded multiplication ideal of R such that qg (qg (M)) = qg (M), and every graded representable multiplication R-module is finitely generated.Keywords : Graded multiplication modules, Graded ideal qg (M), Graded secondary modules