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Rings Whose Nilpotent Elements form a Levitzki Radical Ring
Communications in Algebra, 2007It is shown that a locally 2-primal ring, but not 2-primal, can be always constructed from any given a 2-primal ring. Locally 2-primal rings are NI but we show that there are NI rings which are not locally 2-primal. We prove that every minimal noncommutative (locally) 2-primal ring is isomorphic to the 2 by 2 upper triangular matrix ring over GF(2). By
C. Y. Hong +5 more
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Canadian Mathematical Bulletin, 1974
The Levitzki radical, which is fundamental in the study of algebras satisfying a polynomial identity, has been shown to exist in the varieties of alternative and Jordan algebras (see Zhevlakov [8], Zwier [9], and Tsai [7]— for an important application of this radical to alternative algebras satisfying a polynomial identity, see Slater [6]).
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The Levitzki radical, which is fundamental in the study of algebras satisfying a polynomial identity, has been shown to exist in the varieties of alternative and Jordan algebras (see Zhevlakov [8], Zwier [9], and Tsai [7]— for an important application of this radical to alternative algebras satisfying a polynomial identity, see Slater [6]).
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Levitzki Radical for certain Varieties
Canadian Journal of Mathematics, 1979Let A be a nonassociative algebra. We let An denote the subalgebra generated by all products of n elements from A. Inductively we define A(0) = A and A(n+1) = (A(n))2. We say that A is nilpotent if, for some n, An = {0}. A is solvable if A(n) = {0} for some n.
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Theorems of Amitsur and Levitzki on Radicals
2004In the 1940s and 1950s the main topics in ring theory were radical theory, nilpotence, algebraicity and local finiteness. It is no surprise that the early work of S.A. Amitsur, J. Levitzki, and I. Kaplansky on PI-rings addressed these topics. They were able to give positive answers for PI-rings to questions which remained open or had negative answers ...
Vesselin Drensky, Edward Formanek
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
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