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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
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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
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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
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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
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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
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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.
Al-Zoubi, Khaldoun, Sharafat, Nisreen
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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
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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
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Tight closure and plus closure for cones over elliptic curves [PDF]
, 2005 We characterize the tight closure of graded primary ideals in a homogeneous coordinate ring over an elliptic curve by numerical conditions and we show that it is in positive characteristic the same as the plus closure.Comment: Some minor ...
Brenner, Holger
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Powers of ideals and the cohomology of stalks and fibers of morphisms [PDF]
, 2012 We first provide here a very short proof of a refinement of a theorem of Kodiyalam and Cutkosky, Herzog and Trung on the regularity of powers of ideals.
Chardin, Marc
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