Results 121 to 130 of about 375 (165)

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.
openaire   +1 more source

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