๐‘บ-closed and saturated subsets in ๐‘ด๐‘ฝ-Modules

Document Type : Original Article

Authors

1 Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran

2 Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran

3 Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, first (by the notions which defined,) we get some new properties and characterizations in MV-modules. We show that there exits an one to one corresponding between P-prime A-ideals of an A-module M and P_S –prime A_S-ideals of M_S, where S is a closed subset of A and P is a prime ideal of A such that Pโ‹‚S=∅. After that we introduced some new notions like subsets (N:_M a), (N:_M I) and by them we find new characterizations for prime A-ideals. We proved that a proper A-ideal N of an A-module M is a prime A-ideal, if and only if for any a∈A\(N:_A M), (N:_M a)=N. Also, we defined the notions S-closed subset and saturated subset of A-modules and find some characterizations for them. We show that for multiplicative closed subset S of A and S-closed subset S^* of a finitely generated A-module M, if N is an A-ideal of M which is maximal in ใ€–M\Sใ€—^* and the ideal (N:M) is maximal in A\S, then N is a prime A-ideal of M such that ( N_Sโˆถ_(A_S ) M_S )=(N:_A M)_S.

Keywords

References

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Fuzzy Systems and its Applications
Volume 5, Issue 1 - Serial Number 10
August 2022
Pages 269-293

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History

  • Receive Date: 19 June 2022
  • Revise Date: 11 August 2022
  • Accept Date: 23 September 2022

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