AU - Ansari, A. U.
AU - Sharma, B. K.
AU - Kumar, Sh. D.
AU - Behara, S.
TI - Graded Prime Ideals Attached to a Group Graded Module
PT - JOURNAL ARTICLE
TA - IJMSI
JN - IJMSI
VO - 17
VI - 2
IP - 2
4099 - http://ijmsi.ir/article-1-1415-en.html
4100 - http://ijmsi.ir/article-1-1415-en.pdf
SO - IJMSI 2
ABĀ - 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.
CP - IRAN
IN - Department of Mathematics, University of Allahabad, Prayagraj, India
LG - eng
PB - IJMSI
PG - 59
PT - Research paper
YR - 2022