On weakly S-prime ideals of commutative rings-Reference-Cited by-同舟云学术

On weakly S-prime ideals of commutative rings

Published:2021-06-01 Issue:2 Volume:29 Page:173-186
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Almahdi Fuad Ali Ahmed¹,Bouba El Mehdi²,Tamekkante Mohammed³

Affiliation:

1. Department of Mathematics, Faculty of Science , King Khalid University , P.O. Box. 9004 , Abha , Saudi Arabia .

2. Team of Modeling and Scientific Computing, Mathematics Department, Pluridisciplinary faculty , Mohammed First University , B.P. 300, Selouane, Nador 62700 , Morocco .

3. Department of Mathematics, Faculty of Science , University Moulay Ismail Meknes , Box 11201 , Zitoune , Morocco .

Abstract

Abstract Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R, if 0 ≠ ab ∈ P, then sa ∈ P or sb ∈ P. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/auom-2021-0024

Reference10 articles.

1. [1] D.D. Anderson, E. Smith, Weakly prime ideals, Houston J. Math. 29 (2003) 831840.

2. [2] A. Badawi, U. Tekir and E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Korean Math. Soc., 51(4) (2014), 1163–1173.

3. [3] M. D’Anna, A construction of Gorenstein rings, J. Algebra 306(6) (2006), 507–519.

4. [4] M. D’Anna and M. Fontana, An amalgamated duplication of a ring along an ideal: the basic properties, J. Algebra Appl. 6(3) (2007), 443–459.

5. [5] M. D’Anna and M. Fontana, The amalgamated duplication of a ring along a multiplicative-canonical ideal, Ark. Mat. 45(2) (2007), 241–252.

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