Shahabaddin Ebrahimi ATANI, Reza Ebrahimi Atani

11586

Graded multiplication modules and the graded ideal qg (M)

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.

Anahtar Kelimeler:

Graded multiplication modules, Graded ideal qg (M), Graded secondary modules

Graded multiplication modules and the graded ideal qg (M)

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,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

Arşiv

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