Results 111 to 120 of about 184 (133)
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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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Functional equations related to higher derivations in semiprime rings
Open Mathematics, 2021O H Ezzat
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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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On derivations and commutativity in semiprime rings
Communications in Algebra, 1995Howard E Bell
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ON GENERALIZED DERIVATIONS OF PRIME AND SEMIPRIME RINGS
Taiwanese Journal of Mathematics, 2012Shuliang Huang
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Nilpotent and invertible values in semiprime rings with generalized derivations
Aequationes Mathematicae, 2011Shakir Ali +2 more
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Derivations with engel conditions in prime and semiprime rings
Czechoslovak Mathematical Journal, 2012Shuliang Huang
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