• P M SRINIVAS

Assume that G is a group and that R is a commutative ring that belongs to G. The concept of the related graded ideal g (M) of R is defined for a graded R-module. It has been established that studying graded multiplication modules requires knowledge of the graded ideal g (M). The conclusions are as follows, which are supported by the numerous applications given: if M is a graded faithful multiplication module, then g (M) is an idempotent graded multiplication ideal of R such that g (g (M)) = g (M), and any graded representable multiplication R -module is finitely produced.

Commutative Ring, Graded Ideal, Graded R Module, Multiplication R-module

"Graded multiplication modules and the graded ideal ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.9, Issue 9, page no.a894-a897, September-2022, Available :http://www.jetir.org/papers/JETIR2209095.pdf

"Graded multiplication modules and the graded ideal ", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.9, Issue 9, page no. ppa894-a897, September-2022, Available at : http://www.jetir.org/papers/JETIR2209095.pdf