AU - Ansari, A. U. AU - Sharma, B. K. AU - Kumar, Sh. D. AU - Behara, S. TI - Graded Prime Ideals Attached to a Group Graded Module PT - JOURNAL ARTICLE TA - IJMSI JN - IJMSI VO - 17 VI - 2 IP - 2 4099 - http://ijmsi.ir/article-1-1415-en.html 4100 - http://ijmsi.ir/article-1-1415-en.pdf SO - IJMSI 2 ABĀ  - Let $G$ be a finitely generated abelian group and $M$ be a $G$-graded $A$-module. In general, $G$-associated prime ideals to $M$ may not exist. In this paper, we introduce the concept of $G$-attached prime ideals to $M$ as a generalization of $G$-associated prime ideals which gives a connection between certain $G$-prime ideals and $G$-graded modules over a (not necessarily $G$-graded Noetherian) ring. We prove that the $G$-attached prime ideals exist for every nonzero $G$-graded module and this generalization is proper. We transfer many results of $G$-associated prime ideals to $G$-attached prime ideals and give some applications of it. CP - IRAN IN - Department of Mathematics, University of Allahabad, Prayagraj, India LG - eng PB - IJMSI PG - 59 PT - Research paper YR - 2022