Results 221 to 230 of about 1,454,781 (239)

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 and Radicals in Rings Graded by Clifford Semigroups

Communications in Algebra, 1997
In 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
exaly   +2 more sources

Prime Ideals of Rings Graded by a Commutative Semigroup Which Is a Nilpotent Extension of a Group

Honam Mathematical Journal, 2007
We study the prime ideal structure of the direct sum of directed system of rings indexed by a commutative semigroup which is nilpotent extension of a group.
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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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Graded 1-Absorbing Prime Ideals of Graded Commutative Rings

Journal of Algebra and Its Applications, 2023
Mohammed Issoual
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