Results 151 to 160 of about 206 (186)

On rings with xn − x nilpotent

Journal of Algebra and Its Applications, 2021
For [Formula: see text] and for a ring [Formula: see text] the notation [Formula: see text] means that [Formula: see text] is nilpotent for all [Formula: see text]. In this paper, rings [Formula: see text] for which [Formula: see text] holds are completely characterized for any integers [Formula: see text]. This answers a question which was raised in [
A. N. Abyzov, D. T. Tapkin
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Nilpotent Ideals in Alternative Rings

Canadian Mathematical Bulletin, 1980
It is well known and immediate that in an associative ring a nilpotent one-sided ideal generates a nilpotent two-sided ideal. The corresponding open question for alternative rings was raised by M. Slater [6, p. 476]. Hitherto the question has been answered only in the case of a trivial one-sided ideal J (i.e., in case J2 = 0) [5]. In this note we solve
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On almost nilpotent rings

Acta Mathematica Hungarica, 1985
In their paper [Acta Math. Acad. Sci. Hung. 39, 11-15 (1982; Zbl 0441.16006)] \textit{G. A. P. Heyman}, \textit{T. L. Jenkins} and \textit{H. J. Le Roux} investigated the classes \(\alpha_ 1,\alpha_ 2,\alpha_ 3\) resp. of rings R such that every non-zero subring, left ideal, ideal resp. of R strictly contains a power of R.
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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 prime (−1,1) rings

Asian-European Journal of Mathematics, 2016
Let [Formula: see text] be a 2, 3-torsion-free prime [Formula: see text] ring with commutative center [Formula: see text]. If [Formula: see text] is not contained in the nucleus [Formula: see text], then a ring defined by a new product [Formula: see text] is nilpotent of index at most 11.
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Homology of Free Nilpotent Lie Rings

Journal of Mathematical Sciences, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Jordan nilpotency in group rings

Journal of Group Theory, 2013
Abstract. We investigate the Jordan nilpotency of a group ring RG and, when RG has an involution that is the linear extension of an involution on G, also the Jordan nilpotency of the symmetric elements in RG.
Edgar G. Goodaire, César Polcino Milies
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A Note on Nilpotent Jordan Rings

Canadian Mathematical Bulletin, 1987
AbstractLet R be a 2-torsion free associative ring with involution. It is shown that if the set S of symmetric elements is nilpotent as a Jordan ring then R is nilpotent.
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Artinian rings with nilpotent adjoint group

Ukrainian Mathematical Journal, 2006
Summary: Let \(R\) be an Artinian ring (not necessarily with unit element), let \(Z(R)\) be its center, and let \(R^\circ\) be the group of invertible elements of the ring \(R\) with respect to the operation \(a\circ b=a+b+ab\). We prove that the adjoint group \(R^\circ\) is nilpotent and the set \(Z(R)+R^\circ\) generates \(R\) as a ring if and only ...
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Nilpotent Artinian rings

Publicationes Mathematicae Debrecen, 2022
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