Graded Prime Ideals Attached to a Group Graded Module

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Ansari Ajim Uddin; SHARMA B.K.; Datt Kumar Shiv; Behara Srinivas

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Journal Paper

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2022 | Volume:17 | Issue:2 Page(s): 59-74

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Title

Graded Prime Ideals Attached to a Group Graded Module

Author(s)

Ansari Ajim Uddin | SHARMA B.K. | Datt Kumar Shiv | Behara Srinivas | Issue Writer Certificate

Keywords

graded module

associated prime ideal

attached prime ideal

Weak G

attached prime ideal

Abstract

Let G be a , nitely 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.

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APA: Copy

Ansari, Ajim Uddin, SHARMA, B.K., Datt Kumar, Shiv, & Behara, Srinivas. (2022). Graded Prime Ideals Attached to a Group Graded Module. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 17(2), 59-74. SID. https://sid.ir/paper/1004780/en

Vancouver: Copy

Ansari Ajim Uddin, SHARMA B.K., Datt Kumar Shiv, Behara Srinivas. Graded Prime Ideals Attached to a Group Graded Module. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2022;17(2):59-74. Available from: https://sid.ir/paper/1004780/en

IEEE: Copy

Ajim Uddin Ansari, B.K. SHARMA, Shiv Datt Kumar, and Srinivas Behara, “Graded Prime Ideals Attached to a Group Graded Module,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 17, no. 2, pp. 59–74, 2022, [Online]. Available: https://sid.ir/paper/1004780/en

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