Results 1 to 10 of about 549 (90)
Mathematics, 2021 The purpose of this paper is to introduce the concept of graded 2-prime ideals as a new generalization of graded prime ideals. We show that graded 2-prime ideals and graded semi-prime ideals are different.
Malik Bataineh, Rashid Abu-Dawwas
doaj +5 more sources
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 +4 more sources
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 +3 more sources
Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings
MathematicsIn this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous
Azzh Saad Alshehry +2 more
doaj +4 more sources
On Graded S-Primary Ideals [PDF]
Mathematics, 2021 Let R be a commutative graded ring with unity, S be a multiplicative subset of homogeneous elements of R and P be a graded ideal of R such that P⋂S=∅.
Azzh Saad Alshehry
doaj +2 more sources
ON GRADED 2-ABSORBING PRIMARY AND GRADED WEAKLY 2-ABSORBING PRIMARY IDEALS
Journal of the Korean Mathematical Society, 2017 Summary: Let \(G\) be a group with identity \(e\) and let \(R\) be a \(G\)-graded ring. In this paper, we introduce and study graded 2-absorbing primary and graded weakly 2-absorbing primary ideals of a graded ring which are different from 2-absorbing primary and weakly 2-absorbing primary ideals.
Khaldoun Al-Zoubi
exaly +4 more sources
Primary ideals with good associated graded ring
Journal of Pure and Applied Algebra, 2000 Let \((A,{\mathcal M})\) be a local Cohen-Macaulay ring of dimension \(d>0\), let \(I\) be an \({\mathcal M}\)-primary ideal of \(A\), \(J\) be the ideal generated by a maximal superficial sequence for \(I\), and let \(G\) be the associated graded ring of \(I\). For a natural number \(k\), the ideal \(I\) is said to be \(k\)-standard if \(I^n\cap J=JI^{
exaly +2 more sources
Generalizations of graded S-primary ideals
Proyecciones (Antofagasta), 2022 The goal of this article is to present the graded weakly S-primary ideals and graded g-weakly S-primary ideals which are extensions of graded weakly primary ideals. We state P is a graded weakly S-primary ideal of R if there exists s ∈ S such that for all x,y ∈ h(R), if 0 ̸= xy ∈ P, then sx ∈ P or sy ∈ Grad(P). Several properties and characteristics of
Al-Shorman, Tamem +2 more
openaire +3 more sources
WSEAS TRANSACTIONS ON MATHEMATICS, 2021 Let G be a group with identity e and R be a commutative G-graded ring with nonzero unity 1. Graded semi-primary and graded 1-absorbing primary ideals have been investigated and examined by several authors as generalizations of graded primary ideals. However, these three concepts are different.
Alaa Melhem +2 more
openaire +2 more sources