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Semiprime Rings with Hypercentral Derivations

Canadian Mathematical Bulletin, 1995
AbstractLetRbe a semiprime ring with a derivationd, λ a left ideal ofRandk, ntwo positive integers. Suppose that[d(xn),xn]k= 0 for allx∊ λ. Then [λ,R]d(R)= 0. That is, there exists a central idempotente∊U, the left Utumi quotient ring ofR, such thatdvanishes identically oneUand λ(l —e) is central in (1 —e ...
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Semiprime Goldie Generalised Matrix Rings

Canadian Mathematical Bulletin, 1995
AbstractNecessary and sufficient conditions are given for a generalised matrix ring to be semiprime right Goldie.
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Semiprime torsion free rings

2016
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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On Jordan Structure in Semiprime Rings

Canadian Journal of Mathematics, 1976
A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and
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Noetherian Semiprime Rings

1973
A ring S is a (classical) right quotient ring of a subring T if every regular element a ∈ T has an inverse in S and $$ S = \{ a{b^{ - 1}}|a,b \in T,b\;{\text{reular}}\} $$ Then T is an order in S (cf. 7.21). The following condition is necessary and sufficient for a ring T to possess a classical quotient ring: If a, b ∈ T, and if b is regular ...
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On Skew Derivations in Semiprime Rings

Algebras and Representation Theory, 2012
Let \(R\) 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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THE SEMIPRIMENESS OF SEMIGROUP RINGS

JP Journal of Algebra, Number Theory and Applications, 2021
Hirano, Yasuyuki   +2 more
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Gold-Catalyzed Synthesis of Small Rings

Chemical Reviews, 2021
Mauro Mato   +2 more
exaly  

On derivation of semiprime rings

2012
The 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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THE SOURCE OF SEMIPRIMENESS OF RINGS

2018
Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar ...
Aydin, Neset   +2 more
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