TY - JOUR
T1 - Graded Prime Ideals Attached to a Group Graded Module
TT -
JF - IJMSI
JO - IJMSI
VL - 17
IS - 2
UR - http://ijmsi.ir/article-1-1415-en.html
Y1 - 2022
SP - 59
EP - 74
KW - $G$-graded module
KW - $G$-associated prime ideal
KW - $G$-attached prime ideal
KW - Weak $G$-attached prime ideal.
N2 - 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.
M3 10.52547/ijmsi.17.2.59
ER -