Results 141 to 150 of about 206 (186)
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ANNALI DELL'UNIVERSITA' DI FERRARA, 2021
A nonzero sum of a unit and a nilpotent element in a ring is called a fine element, which is also known as nil clean element. Rings in which every nonzero nilpotent is fine, is called \(NF\) rings. In this article \(NF\) rings are thoroughly discussed.
Grigore Călugăreanu, Yiqiang Zhou
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A nonzero sum of a unit and a nilpotent element in a ring is called a fine element, which is also known as nil clean element. Rings in which every nonzero nilpotent is fine, is called \(NF\) rings. In this article \(NF\) rings are thoroughly discussed.
Grigore Călugăreanu, Yiqiang Zhou
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Modules Over Nilpotent Group Rings
Journal of the London Mathematical Society, 1995In the representation theory of finitely generated nilpotent groups the use of induction leads one to consider impervious modules, those modules contain no non-zero submodules induced from a module over a subgroup of infinite index. Let \(H\) be a finitely generated nilpotent group with centre \(Z\) and let \(R\) be a commutative ring. Let \(H_0\) be a
Brookes, C. J. B., Groves, J. R. J.
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Semiprime Rings with Nilpotent Derivatives
Canadian Mathematical Bulletin, 1981There has been a great deal of work recently concerning the relationship between the commutativity of a ring JR and the existence of certain specified derivations of R. Bell, Herstein, Procesei, Schacher, Ligh, Martindale, Putcha, Wilson, and Yaqub [1, 2, 6, 8, 9, 10, 11, 12, 14] have studied conditions on commutators which imply the commutativity of ...
Chung, L. O., Luh, Jiang
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American Journal of Mathematics, 1991
Let \(F\subset K\) be a field extension. The authors prove a variety of results on Witt rings and Galois cohomology of the ``going-down'' type, i.e. how the behaviour of \(K\) influences that of \(F\). As usual, \(H^ n(F,-)\) denotes the cohomology of the Galois group of a separable algebraic closure of \(F\) and \(F_ q\) the quadratic closure.
Arason, Jón Kr., Elman, Richard
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Let \(F\subset K\) be a field extension. The authors prove a variety of results on Witt rings and Galois cohomology of the ``going-down'' type, i.e. how the behaviour of \(K\) influences that of \(F\). As usual, \(H^ n(F,-)\) denotes the cohomology of the Galois group of a separable algebraic closure of \(F\) and \(F_ q\) the quadratic closure.
Arason, Jón Kr., Elman, Richard
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GENERALIZED LIE NILPOTENT GROUP RINGS
Mathematics of the USSR-Sbornik, 1987Translation from Mat. Sb., Nov. Ser. 129(171), No.1, 154-158 (Russian) (1986; Zbl 0601.16011).
Bovdi, A. A., Khripta, I. I.
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Israel Journal of Mathematics, 1971
In this note we introduce a class of nil rings (called essentially nilpotent) which properly contains the class of nilpotent rings. A nil ring is said to be essentially nilpotent if it contains an essential right ideal which is nilpotent. Various properties of essentially nilpotent rings are investigated. A nil ring is essentially nilpotent if and only
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In this note we introduce a class of nil rings (called essentially nilpotent) which properly contains the class of nilpotent rings. A nil ring is said to be essentially nilpotent if it contains an essential right ideal which is nilpotent. Various properties of essentially nilpotent rings are investigated. A nil ring is essentially nilpotent if and only
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RINGS OVER WHICH COEFFICIENTS OF NILPOTENT POLYNOMIALS ARE NILPOTENT
International Journal of Algebra and Computation, 2011Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, observing the structure of nilpotent elements in Armendariz rings and introducing the notion of nil-Armendariz rings. The class of nil-Armendariz rings contains Armendariz rings and NI rings.
Kwak, Tai Keun, Lee, Yang
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Rings generalized by tripotents and nilpotents
Czechoslovak Mathematical Journal, 2022Several characterizations of a nil-clean-type condition first studied by \textit{Y. Zhou} in [J. Algebra Appl. 17, No. 1, Article ID 1850009, 7 p. (2018; Zbl 1415.16034)] are established. A ring \(R\) is called \emph{Zhou nil-clean} if every element of \(R\) is a sum of a nilpotent element and two tripotent elements that all commute. (Tripotence is the
Chen, Huanyin +2 more
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IDENTITIES IN ALMOST NILPOTENT LIE RINGS
Mathematics of the USSR-Sbornik, 1983The following Lie rings are shown to have finite bases for their identities. (i) has a finite ideal with nilpotent. (ii) has a nilpotent ideal of finite index with nilpotent on for each . (iii) is soluble, algebraic and possesses a nilpotent ideal of finite index.
Volkov, M. V., Gejn, A. G.
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Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1982
SynopsisThe class of M-nilpotent rings is defined as a generalisation of the class of T-nilpotent rings. Certain results for radicals of T-nilpotent rings are shown to hold also in this larger class of rings.
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SynopsisThe class of M-nilpotent rings is defined as a generalisation of the class of T-nilpotent rings. Certain results for radicals of T-nilpotent rings are shown to hold also in this larger class of rings.
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