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Prime Ideals in Strongly Graded Rings by Polycyclic-by-finite Groups II
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On graded 1-absorbing prime ideals
São Paulo Journal of Mathematical Sciences, 2021Let \(R\) be a commutative ring graded by a group. A graded 1-absorbing prime ideal of \(R\) is defined by the authors as being a proper graded ideal \(P\) such that for any non-invertible homogeneous elements \(x,y,z\in P\), either \(xy\in P\) or \(z\in P\). Several basic results and equivalent characterizations of such ideals are presented.
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An intersection condition for graded prime ideals
Bollettino dell'Unione Matematica Italiana, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Al-Zoubi, Khaldoun, Qarqaz, Feda'a
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On graded-(m, n)-prime ideals of commutative graded rings
Rendiconti del Circolo Matematico di Palermo Series 2Let \(G\) be an abelian group written additively, and let \(R\) be a commutative \(G\)-graded ring with identity. Let \(m\) and \(n\) be positive integers. The authors in this paper introduced a new class of ideals, called graded \((m, n)\)-prime ideals, which properly lies between the classes of graded-prime ideals and the graded \((m, n)\)-closed ...
Anass Assarrar, Najib Mahdou
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Prime ideals and radicals in rings graded by clifford semigroups
Communications in Algebra, 1997In this paper we continue our study of the ideal structure of the direct sum of a directed system of rings indexed by a semigroup begun In [1], with emphasis on describing the prime ideals and radicals of semigroup rings and semigroup–graded rings. This time we concentrate on semigroups that fail to satisfy condition (†) of our orginal article but have
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Graded 1-absorbing prime ideals of graded commutative rings
Journal of Algebra and Its Applications, 2021Let G be a group with identity e and R be G-graded commutative ring with [Formula: see text] In this paper, we introduce and study the graded versions of 1-absorbing prime ideal. We give some properties and characterizations of these ideals in graded ring, and we give a characterization of graded 1-absorbing ideal the idealization [Formula: see text]
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