Results 171 to 180 of about 1,744,733 (206)
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Nilpotent elements of a free Jordan algebra
Siberian Mathematical Journal, 1985The 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.
Yu A Medvedev
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Central subalgebras of the centralizer of a nilpotent element
Proceedings of the American Mathematical Society, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mcninch, George J., Testerman, Donna M.
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A left 3-Engel element whose normal closure is not nilpotent [PDF]
Journal of Pure and Applied Algebra, 2020 We give an example of a locally nilpotent group G containing a left 3-Engel element x where 〈x〉G is not ...
Marialaura Noce +2 more
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When nilpotent elements generate nilpotent ideals
Journal of Algebra and Its Applications, 2023We 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, 2017Let [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, 2012We 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, 1996AbstractIn this paper we study in which rings a non-zero idempotent element can be presented as a sum of two nilpotent elements.
Ferrero, M. +2 more
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Nilpotent elements and McCoy rings
Studia Scientiarum Mathematicarum Hungarica, 2012We 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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AN EXAMPLE OF A CHAIN PRIME RING WITH NILPOTENT ELEMENTS
Mathematics of the USSR-Sbornik, 1984Translation from Mat. Sb., Nov. Ser. 120(162), No.3, 441-447 (Russian) (1983; Zbl 0517.16002).
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A Description of Ad-nilpotent Elements in Semiprime Rings with Involution
Bulletin of the Malaysian Mathematical Sciences Society, 2021José Brox +2 more
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