Results 161 to 170 of about 40,826 (196)

When nilpotent elements generate nilpotent ideals

Journal of Algebra and Its Applications, 2023
We study the natural class of rings where each nilpotent element generates a nilpotent ideal, calling them the strongly 2-primal rings. We derive many basic properties of these rings, analyze their behavior under standard ring constructions and extensions, and taxonomize their relationship to other natural generalizations of commutativity.
Nielsen, Pace P., Szabo, Steve
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On nilpotent elements of ore extensions

Asian-European Journal of Mathematics, 2017
Let [Formula: see text] be an associative ring with unity, [Formula: see text] be an endomorphism of [Formula: see text] and [Formula: see text] an [Formula: see text]-derivation of [Formula: see text]. We introduce the notion of [Formula: see text]-nilpotent p.p.-rings, and prove that the [Formula: see text]-nilpotent p.p.-condition extends to ...
Azimi, Masoud, Moussavi, Ahmad
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Nilpotent Elements and Skew Polynomial Rings

Algebra Colloquium, 2012
We study the structure of the set of nilpotent elements in extended semicommutative rings and introduce nil α-semicommutative rings as a generalization. We resolve the structure of nil α-semicommutative rings and obtain various necessary or sufficient conditions for a ring to be nil α-semicommutative, unifying and generalizing a number of known ...
Alhevaz, A., Moussavi, A., Hashemi, E.
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Nilpotent elements and McCoy rings

Studia Scientiarum Mathematicarum Hungarica, 2012
We introduce the concept of nil-McCoy rings to study the structure of the set of nilpotent elements in McCoy rings. This notion extends the concepts of McCoy rings and nil-Armendariz rings. It is proved that every semicommutative ring is nil-McCoy. We shall give an example to show that nil-McCoy rings need not be semicommutative. Moreover, we show that
Liang Zhao, Xiaosheng Zhu, Qinqin Gu
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Nilpotent elements in medial semigroups

Mathematica Slovaca, 2019
AbstractWe show without the Kuratowski-Zorn lemma that the set of all nilpotent elements of a medial semigroup (with zero) is the set-theoretic intersection of all its prime ideals. Moreover, some applications of the above theorem are given.
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A Description of Ad-nilpotent Elements in Semiprime Rings with Involution

Bulletin of the Malaysian Mathematical Sciences Society, 2021
Jose Brox   +2 more
exaly  

Nilpotent Elements in Hochschild Cohomology

2018
We study the algebra \(A=K\langle x, y\rangle /(x^2, y^2, (xy)^k+q(yx)^k)\) over the field K where \(k\ge 1\) and where \(0\ne q \in K\). We determine a minimal projective bimodule resolution of A. In the case when q is not a root of unity, we compute its Hochschild cohomology.
openaire   +1 more source

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