Results 111 to 118 of about 179 (118)
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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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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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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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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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Semiprime rings with differential identities
1992Let \(R\) be a semi-prime ring with maximal right quotient ring \(U\) and let \(\text{Der}(U)\) be the set of derivations of \(U\). The extended centroid of \(R\) is \(C\), the center of \(U\). A differential polynomial is an element \(f \in U*_ C C\{X^ W\}\), the free product over \(C\) of \(U\) and the free \(C\)-algebra in indeterminates \(x_ i^ w\),
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