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THE SEMIPRIMENESS OF SEMIGROUP RINGS
JP Journal of Algebra, Number Theory and Applications, 2021Hirano, Yasuyuki +2 more
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Mathematical Journal of Okayama University, 1995
In an earlier paper, the author developed a theory that in a semiprime torsion free ring, there is an essential direct sum of three completely unique and algebraically very different types of ideals, one of which is discrete and the others are continuous.
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In an earlier paper, the author developed a theory that in a semiprime torsion free ring, there is an essential direct sum of three completely unique and algebraically very different types of ideals, one of which is discrete and the others are continuous.
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Additive n-commuting maps on semiprime rings
Proceedings of the Edinburgh Mathematical Society, 2019Let R be a semiprime ring with the extended centroid C and Q the maximal right ring of quotients of R. Set [y, x]1 = [y, x] = yx − xy for x, y ∈ Q and inductively [y, x]k = [[y, x]k−1, x] for k > 1. Suppose that f : R → Q is an additive map satisfying [f(
Cheng-Kai Liu
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On Skew Derivations in Semiprime Rings
Algebras and Representation Theory, 2012Let \(R\) be a ring with center \(Z(R)\), and let \(\sigma\) be an endomorphism of \(R\). An additive map \(\delta\colon R\to R\) is called a \(\sigma\)-derivation if \(\delta(xy)=\sigma(x)\delta(y)+\delta(x)y\) for all \(x,y\in R\). The principal result of the paper, which generalizes a result of the reviewer and \textit{M. N. Daif} [Can. Math.
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Note on Lie ideals with symmetric bi-derivations in semiprime rings
Indian journal of pure and applied mathematics, 2022E. K. Sögütcü, Shuliang Huang
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Some identities related to multiplicative (generalized)-derivations in prime and semiprime rings
Rendiconti del Circolo Matematico di Palermo Series 2, 2022B. Dhara, S. Kar, Nripendu Bera
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On derivation of semiprime rings
2012The paper purports to prove several commutativity theorems for prime or semiprime rings satisfying certain constraints involving derivations, one such being that for some derivation \(d\), \(xyx+d(xyx)=x^2y+d(x^2y)\) for all \(x,y\in R\). Unfortunately the proofs are wrong.
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On semiprime Noetherian PI-rings
Mathematical Journal of Okayama University, 2000Let \(R\) be a semiprime Noetherian PI-ring, and let \(Q\) be its semisimple Artinian classical quotient ring. The author establishes the equivalence of the following three statements. (1) The (classical) Krull dimension of \(R\) is \(\leq 1\); (2) If \(T\) is a ring with \(R\subseteq T\subseteq Q\), then \(T\) is Noetherian; (3) For central regular ...
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On one sided ideals of a semiprime ring with generalized derivations
, 2013Asma Ali, V. De Filippis, F. Shujat
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A Description of Ad-nilpotent Elements in Semiprime Rings with Involution
, 2021Jose Brox +4 more
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