RT - Journal Article
T1 - Graded Prime Ideals Attached to a Group Graded Module
JF - IJMSI
YR - 2022
JO - IJMSI
VO - 17
IS - 2
UR - http://ijmsi.ir/article-1-1415-en.html
SP - 59
EP - 74
K1 - $G$-graded module
K1 - $G$-associated prime ideal
K1 - $G$-attached prime ideal
K1 - Weak $G$-attached prime ideal.
AB - 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.
LA eng
UL http://ijmsi.ir/article-1-1415-en.html
M3 10.52547/ijmsi.17.2.59
ER -