Results 11 to 20 of about 157 (150)
On Graded $ϕ$-$1$-absorbing prime ideals
, 2021 Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity and $GI(R)$ be the set of all graded ideals of $R$. Suppose that $ϕ:GI(R)\rightarrow GI(R)\cup\{\emptyset\}$ is a function. In this article, we introduce and study the concept of graded $ϕ$-$1$-absorbing prime ideals. A proper graded ideal $I$ of $R$ is called a graded $ϕ$% -$1$
Abu-Dawwas, Rasliid +5 more
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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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The Rank-One property for free Frobenius extensions
Comptes Rendus. Mathématique, 2023 A conjecture by the second author, proven by Bonnafé–Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one over $\mathbb{Q}$ when restricted to each block of the algebra.In this ...
Bellamy, Gwyn, Thiel, Ulrich
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Generalizations Of Graded Prime Ideals Over Graded Near Rings
, 2022 This paper considers graded near-rings over a monoid G as a generalizations of the graded rings over groups, introduce certain innovative graded weakly prime ideals and graded almost prime ideals as a generalizations of graded prime ideals over graded near-rings, and explore their various properties and their generalizations in graded near-rings.
Bataineh, Malik +2 more
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Multidegrees, prime ideals, and non-standard gradings
Advances in Mathematics, 2023 to appear in Advances in ...
Caminata A., Cid-Ruiz Y., Conca A.
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Graded Prime Ideals Over Graded Near Ring
, 2022 In this paper, we consider graded near-rings over a monoid $G$ as a generalizations of graded rings over groups. We introduce certain innovative graded prime ideals and study some of its basic properties over graded near-rings.
Bataineh, Malik +2 more
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The chain property for the associated primes of $\CA$-graded ideals [PDF]
Mathematical Research Letters, 2000 We investigate how the chain property for the associated primes of monomial degenerations of toric (or lattice) ideals can be generalized to arbitrary A-graded ideals. The generalization works in dimension d=2, but it fails for d>2.
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Zariski topology on the spectrum of graded classical prime submodules
Applied General Topology, 2013 Let $R$ be a $G$-graded commutative ring with identity and let $M$ be a graded $R$-module. A proper graded submodule $N$ of $M$ is called graded classical prime if for every $a, b\in h(R)$, $m\in h(M)$, whenever $abm\in N$, then either $am\in N$ or $bm ...
Ahmad Yousefian Darani, Shahram Motmaen
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International Journal of Mathematical Analysis, 2014 Let G be an arbitrary group with identity e and let R be a G-graded commutative ring. In this paper, we introduce the concept of graded quasi-prime ideal and we give a number of results concerning such ideals. In fact, our objective is to investigate graded quasi-prime ideals and examine in particular when graded ideals of R are graded quasi-prime ...
Khaldoun Al-Zoubi, Rashid Abu-Dawwas
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Properties of ϕ-Primal Graded Ideals
Journal of Mathematics, 2017 Let R be a commutative graded ring with unity 1≠0. A proper graded ideal of R is a graded ideal I of R such that I≠R. Let ϕ:I(R)→I(R)∪{∅} be any function, where I(R) denotes the set of all proper graded ideals of R.
Ameer Jaber
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