Abstract
Let R be a commutative ring with 1 ≠ 0. In this article, we introduce the concept of weakly (m, n)−closed δ−primary ideals of R and explore its basic properties. We show that a proper ideal I of R is a weakly (m, n)−closed γ ◦ δ−primary ideal of R if and only if I is an (m, n)−closed γ ◦ δ−primary ideal of R, where δ and γ are expansions ideals of R with δ(0) is an (m, n)−closed γ−primary ideal of R. Furthermore, we provide examples to demonstrate the validity and applicability of our results.
Publisher
Universidad Catolica del Norte - Chile
Reference18 articles.
1. [1] D. D. Anderson and M. Bataineh, "Generalizations of prime ideals", Communications in Algebra, vol. 36, no. 2, pp. 686-696, 2008. doi: 10.1080/00927870701724177
2. [2] D. D. Anderson and E. Smith, "Weakly prime ideals", Houston Journal of Mathematics, vol. 29, no. 4, pp. 831-840, 2003.
3. [3] D. F. Anderson and A. Badawi, "On (m, n)−closed ideals of commutative rings", Journal of Algebra and Its Applications, vol. 16, no. 1, 1750013, 21 pp., 2017. doi: 10.1142/S021949881750013X
4. [4] D. F. Anderson and A. Badawi, "On n−absorbing ideals of commutative rings", Communications in Algebra, vol. 39, no. 5, pp. 1646-1672, 2011. doi: 10.1080/00927871003738998
5. [5] D. F. Anderson and A. Badawi and B. Fahid, "Weakly (m, n)−closed ideals and (m, n)−Von Neumann Regular Rings", Journal of the Korean Mathematical Society, vol. 55, no. 5, pp. 1031-1043, 2018. doi: 10.4134/JKMS.j170342
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