%0 Journal Article
%A Ansari, A. U.
%A Sharma, B. K.
%A Kumar, Sh. D.
%A Behara, S.
%T Graded Prime Ideals Attached to a Group Graded Module
%J Iranian Journal of Mathematical Sciences and Informatics
%V 17
%N 2
%U http://ijmsi.ir/article-1-1415-en.html
%R 10.52547/ijmsi.17.2.59
%D 2022
%K $G$-graded module, $G$-associated prime ideal, $G$-attached prime ideal, Weak $G$-attached prime ideal.,
%X 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.
%> http://ijmsi.ir/article-1-1415-en.pdf
%P 59-74
%& 59
%!
%9 Research paper
%L A-10-3880-1
%+ Department of Mathematics, University of Allahabad, Prayagraj, India
%G eng
%@ 1735-4463
%[ 2022