Results 1 to 10 of about 48 (48)
On weakly S-prime ideals of commutative rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 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
Almahdi Fuad Ali Ahmed +2 more
doaj +1 more source
On (1,2)-absorbing primary ideals and uniformly primary ideals with order ≤ 2
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 This paper introduces a subset of the set of 1-absorbing primary ideals introduced in [3]. An ideal I of a ring R is (1,2)-absorbing primary if, whenever non-unit elements α, β, γ ∈ R with αβγ ∈ I,then αβ ∈ I or γ2 ∈ I.
Alhazmy Khaled +3 more
doaj +1 more source
Extended Annihilating-Ideal Graph of a Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2022 Let R be a commutative ring with identity. An ideal I of a ring R is called an annihilating-ideal if there exists a nonzero ideal J of R such that IJ = (0) and we use the notation 𝔸(R) for the set of all annihilating-ideals of R.
Nithya S., Elavarasi G.
doaj +1 more source
Semi r-ideals of commutative rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 For commutative rings with identity, we introduce and study the concept of semi r-ideals which is a kind of generalization of both r-ideals and semiprime ideals.
Khashan Hani A., Celikel Ece Yetkin
doaj +1 more source
Some notes on graded weakly 1-absorbing primary ideals
Demonstratio Mathematica, 2023 A proper graded ideal PP of a commutative graded ring RR is called graded weakly 1-absorbing primary if whenever x,y,zx,y,z are nonunit homogeneous elements of RR with 0≠xyz∈P0\ne xyz\in P, then either xy∈Pxy\in P or zz is in the graded radical of PP. In
Alshehry Azzh Saad +2 more
doaj +1 more source
Graded weakly 1-absorbing primary ideals
Demonstratio Mathematica, 2023 Let GG be a group and RR be a GG-graded commutative ring with nonzero unity 1. In this article, we introduce the concept of graded weakly 1-absorbing primary ideals which is a generalization of graded 1-absorbing primary ideal.
Bataineh Malik, Abu-Dawwas Rashid
doaj +1 more source
SP-Domains are Almost Dedekind — A Streamlined Proof
Discussiones Mathematicae - General Algebra and Applications, 2020 Let D be a domain. By [4], D has “property SP” if every ideal of D is a product of radical ideals. It is natural to consider property SP after studying Dedekind domains, which involve factoring ideals into prime ideals.
Ahmed Malik Tusif
doaj +1 more source
On the metric dimension of a total graph of non-zero annihilating ideals
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R − {0} such that Ir = (0). Visweswaran and H. D.
Abachi Nazi, Sahebi Shervin
doaj +1 more source
On 2-Absorbing Primary Submodules of Modules over Commutative Rings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016 All rings are commutative with 1 ≠ 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an
Mostafanasab Hojjat +3 more
doaj +1 more source
Some results on the total zero-divisor graph of a commutative ring [PDF]
Arab Journal of Mathematical SciencesPurposeThe purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is ...
Subramanian Visweswaran
doaj +1 more source