نشریه علوم ریاضی و انفورماتیک

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Ansari A U, Sharma B K, Kumar S D, Behara S. Graded Prime Ideals Attached to a Group Graded Module. IJMSI 2022; 17 (2) :59-74
URL: http://ijmsi.ir/article-1-1415-fa.html

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.