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A note on inner and reflexive inverses in semiprime rings
Journal of Algebra and its Applications, 2020Let [Formula: see text] be a semiprime ring, not necessarily with unity, and [Formula: see text]. Let [Formula: see text] (respectively, [Formula: see text]) denote the set of inner (respectively, reflexive) inverses of [Formula: see text] in [Formula ...
Tsiu-Kwen Lee
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Semiprime Rings with Hypercentral Derivations
Canadian Mathematical Bulletin, 1995AbstractLetRbe 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, 1995AbstractNecessary and sufficient conditions are given for a generalised matrix ring to be semiprime right Goldie.
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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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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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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, 1976A 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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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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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, 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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THE SEMIPRIMENESS OF SEMIGROUP RINGS
JP Journal of Algebra, Number Theory and Applications, 2021Hirano, Yasuyuki +2 more
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