Iranian Journal of Mathematical Sciences and Informatics
مجله علوم ریاضی و انفورماتیک
IJMSI
Basic Sciences
http://ijmsi.ir
1
admin
1735-4463
2008-9473
8
10.61186/ijmsi
14
8888
13
en
jalali
1401
6
1
gregorian
2022
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17
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online
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fulltext
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Graded Prime Ideals Attached to a Group Graded Module
تخصصي
Special
پژوهشي
Research paper
<div style="text-align: justify;">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.</div>
$G$-graded module, $G$-associated prime ideal, $G$-attached prime ideal, Weak $G$-attached prime ideal.
59
74
http://ijmsi.ir/browse.php?a_code=A-10-3880-1&slc_lang=en&sid=1
A. U.
Ansari
ajimmatau@gmail.com
`10031947532846009578`

10031947532846009578
Yes
Department of Mathematics, University of Allahabad, Prayagraj, India
B. K.
Sharma
brajeshsharma72@gmail.com
`10031947532846009579`

10031947532846009579
No
Department of Mathematics, University of Allahabad, Prayagraj, India
Sh. D.
Kumar
sdt@mnnit.ac.in
`10031947532846009580`

10031947532846009580
No
Department of Mathematics, Motilal Nehru National Institute of Technology, Prayagraj, India
S.
Behara
srinivasbehara45@gmail.com
`10031947532846009581`

10031947532846009581
No
Government Polytechnic, Gannavaram, Krishna District, Andhra Pradesh, India