Results 221 to 230 of about 1,390,742 (240)

Graded 1-absorbing prime ideals of graded commutative rings

Journal of Algebra and Its Applications, 2021
Let 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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On strongly homogeneous prime ideals in a graded integral domain

Journal of Algebra and Its Applications, 2023
Let [Formula: see text] be a torsionless grading monoid and [Formula: see text] be a [Formula: see text]-graded integral domain. In this paper, we present basic properties and give a complete characterization of strongly homogeneous prime ideals of [Formula: see text].
Abdelkbir Riffi, Chahrazade Bakkari, Najib Mahdou   +2 more
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On prime ideals and radicals of polynomial rings and graded rings

Journal of Pure and Applied Algebra, 2014
All rings in this paper are associative but not necessarily with identity. For a given ring \(A\), the Brown-McCoy radical \(G(A)\) of \(A\) is the intersection of all ideals \(I\) of \(A\) such that the factor ring \(A/I\) is a simple ring with unity and the \(S\)-radical \(S(A)\) of \(A\) is the intersection of all ideals \(I\) of \(A\) such that the
Lee, P.-H., Puczyłowski, E. R.
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Prime ideals and radicals in semigroup-graded rings

Proceedings of the Edinburgh Mathematical Society, 1996
In this paper we study the ideal structure of the direct limit and direct sum (with a special multiplication) of a directed system of rings; this enables us to give descriptions of the prime ideals and radicals of semigroup rings and semigroup-graded rings.We show that the ideals in the direct limit correspond to certain families of ideals from the ...
Bell, Allen D., Stalder, Shubhangi S., Teply, Mark L.   +2 more
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Prime ideals of graded rings and related matters

Communications in Algebra, 1990
Let R be a ring graded by an abelian group.We study prime ideals of R that are maximal for not containing nonzero homogeneous elements.Also prime ideals of the symmetric graded Martindale ring of quotients of R are investigated.The results are applied to study when R is a Jacobson ring in case R is a Z-graded ring or a group ring of a finitely ...
Miguel Ferrero, Eric Jespers, Edmund R. Puczylowski   +2 more
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Prime ideals in strongly graded rings by polycyclic-by-finite groups

Mathematical Journal of Okayama University, 1992
Let \(R*G\) be a crossed product of the polycyclic-by-finite group \(G\) over the prime right Noetherian ring \(R\). In the reviewer's paper [Trans. Am. Math. Soc. 301, 737-759 (1987; Zbl 0619.16007)] the prime ideals of \(R*G\) disjoint from \(R\) were explicitly described in terms of the primes in a certain twisted group algebra.
Marubayashi, Hidetoshi, Miyamoto, Haruo
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Prime and Primitive Ideals in Graded Deformations of Algebraic Quantum Groups at Roots of Unity

Algebras and Representation Theory, 2003
In this work, the author studies the prime and primitive ideals in twists of quantum function algebras at roots of unity.
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On 2-N-prime ideals over commutative Z2-graded ring

Journal of Discrete Mathematical Sciences & Cryptography
Let R be a commutative ring with a nonzero unity element. In this article, we introduce and examine new classes of ideals in Z2-graded rings, expanding upon the earlier concept of N-prime ideals. Using the function N : R → R0, defined by N(x) = x0 2 – x1 2 for x = x0 + x1 ∈ R, we define and analyze two new types of ideals, 2-N-prime and weakly 2-N ...
Alaa Melhem, Rashid Abu-Dawwas, Ali Albalasmeh   +2 more
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On graded 1-absorbing prime submodules

Journal of Discrete Mathematical Sciences and Cryptography, 2023
Rashid Abu-Dawwas
exaly  

The homogeneous spectrum of a $$\mathbb Z_2$$-graded commutative ring

Beitrage Zur Algebra Und Geometrie, 2023
Mohamed Aqalmoun
exaly