Results 191 to 200 of about 1,062 (223)

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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Artinian rings with nilpotent adjoint group

Ukrainian Mathematical Journal, 2006
Нехай R — артинове кільце, необов'язково з одиницею, Z(R) — його центр i R⁰ — група оборотних елементів кільця R відносно операції a о b = a + b + ab. Доводиться, що приєднана група R⁰ нільпотентна та множина Z(R)+R⁰ породжує R як кільце тоді і тільки ...
Евстафьев, Р.Ю.
exaly   +3 more sources

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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On the Representation of an Idempotent as a Sum of Nilpotent Elements

Canadian Mathematical Bulletin, 1996
AbstractIn this paper we study in which rings a non-zero idempotent element can be presented as a sum of two nilpotent elements.
Ferrero, M., Puczyłowski, E. R., Sidki, S.   +2 more
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Nilpotent elements of a free Jordan algebra

Siberian Mathematical Journal, 1985
The author settles the following well-known question: does the free Jordan algebra contain nonzero nilpotent elements ? It is proved that the free countable generated Jordan algebra over a field F of characteristic greater than 7 contains nonzero nilpotent elements and nonzero absolute zero divisors.
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Generalization of Nilpotency of Ring Elements to Module Elements

Communications in Algebra, 2013
We define nilpotent and strongly nilpotent elements of a module M and show that the set 𝒩 s (M) of all strongly nilpotent elements of M over a commutative unital ring R coincides with the classical prime radical β cl (M) the intersection of all classical prime submodules of M.
David Ssevviiri, Nico Groenewald
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AN EXAMPLE OF A CHAIN PRIME RING WITH NILPOTENT ELEMENTS

Mathematics of the USSR-Sbornik, 1984
Translation from Mat. Sb., Nov. Ser. 120(162), No.3, 441-447 (Russian) (1983; Zbl 0517.16002).
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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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Representing nilpotent matrices as single commutators

Communications in Algebra, 2021
Emily Hoopes-Boyd
exaly