@ARTICLE{Ansari, author = {Ansari, A. U. and Sharma, B. K. and Kumar, Sh. D. and Behara, S. and }, title = {Graded Prime Ideals Attached to a Group Graded Module}, volume = {17}, number = {2}, abstract ={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. }, URL = {http://ijmsi.ir/article-1-1415-en.html}, eprint = {http://ijmsi.ir/article-1-1415-en.pdf}, journal = {Iranian Journal of Mathematical Sciences and Informatics}, doi = {10.52547/ijmsi.17.2.59}, year = {2022} }