Turkish Journal of Mathematics
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 \theta_g (M) of R is defined. It is proved that the graded ideal \theta_g (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 \theta_g (M) is an idempotent graded multiplication ideal of R such that \theta_g (\theta_g (M)) = \theta_g (M), and every graded representable multiplication R-module is finitely generated.
DOI
10.3906/mat-0901-22
Keywords
Graded multiplication modules, Graded ideal \theta_g (M), Graded secondary modules
First Page
1
Last Page
9
Recommended Citation
ATANI, S. E, & ATANI, R. E (2011). Graded multiplication modules and the graded ideal \theta_g (M). Turkish Journal of Mathematics 35 (1): 1-9. https://doi.org/10.3906/mat-0901-22
