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 1 - 4 / 41 1.Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, original scientific articleAbstract: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a non-central Lie ideal of ▫$R$▫, and ▫$\delta$▫ a derivation of ▫$R$▫. Suppose that ▫$\alpha$▫ is an automorphism of ▫$R$▫, ▫$D$▫ a skew derivation of ▫$R$▫ with the associated automorphism ▫$\alpha$▫, and ▫$F$▫ a generalized skew derivation of ▫$R$▫ with the associated skew derivation ▫$D$▫. If ▫$$F(x^{m+n}) = F(x^m)x^n + x^m \delta (x^n)$$▫ is a polynomial identity for ▫$L$▫, then either ▫$R$▫ satisfies the standard polynomial identity ▫$s_4(x_1, x_2, x_3, x_4)$▫ of degree 4, or ▫$F$▫ is a generalized derivation of ▫$R$▫ and ▫$\delta = D$▫. Furthermore, in the latter case one of the following statements holds: (1) ▫$D = \delta = 0$▫ and there exists ▫$a \in Q$▫ such that ▫$F(x) = ax$▫ for all ▫$x \in R$▫; (2) ▫$\alpha$▫ is the identical mapping of ▫$R$▫.Found in: ključnih besedahSummary of found: ...fixed positive integers, ▫$R$▫ a 2-torsion free prime ring with the right Martindale quotient ring...Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ringPublished: 15.10.2013; Views: 1931; Downloads: 90 Full text (0,00 KB) 2.Jordan [tau]-derivations of locally matrix ringsChen-Lian Chuang, Ajda Fošner, Tsiu Kwen Lee, 2013, original scientific articleAbstract: Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2 and let ▫$Q_{ms}(R)$▫ be the maximal symmetric ring of quotients of ▫$R$▫. Suppose that ▫$\delta \colon R \to Q_{ms}(R)$▫ is a Jordan ▫$\tau$▫-derivation, where ▫$\tau$▫ is an anti-automorphism of $R$. Then there exists ▫$a \in Q_{ms}(R)$▫ such that ▫$\delta(x) = xa - a\tau(x)$▫ for all ▫$x \in R$▫. Let ▫$X$▫ be a Banach space over the field ▫$\mathbb{F}$▫ of real or complex numbers and let ▫$\mathcal{B}(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫. We prove that ▫$Q_{ms}(\mathcal{B}(X)) = \mathcal{B}(X)$▫, which provides the viewpoint of ring theory for some results concerning derivations on the algebra ▫$\mathcal{B}(X)$▫. In particular, all Jordan ▫$\tau$▫-derivations of ▫$\mathcal{B}(X)$▫ are inner if ▫$\dim_{\mathbb{F}} X>1$▫.Found in: ključnih besedahSummary of found: ...Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2...Keywords: mathematics, algebra, anti-automorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫-derivation, Banach spacePublished: 15.10.2013; Views: 1742; Downloads: 29 Full text (0,00 KB) 3.A note on generalized (m,n)-Jordan centralizersAjda Fošner, 2013, original scientific articleAbstract: The aim of this paper is to define generalized ▫$(m, n)$▫-Jordan centralizers and to prove that on a prime ring with nonzero center and ▫${\rm char}(R) \ne 6mn(m+n)(m+2n)$▫ every generalized ▫$(m, n)$▫-Jordan centralizer is a two-sided centralizer.Found in: ključnih besedahSummary of found: ...centralizers and to prove that on a prime ring with nonzero center and ▫\${\rm char}(R)...Keywords: mathematics, prime ring, semiprime ring, left (right) centralizer, left (right) Jordan centralizer, (m, n)-Jordan centralizer, generalized (m, n)-Jordan centralizerPublished: 15.10.2013; Views: 1736; Downloads: 93 Full text (0,00 KB)This document has more files! More... 4.Prime and semiprime rings with symmetric skew 3-derivationsAjda Fošner, 2013, original scientific articleAbstract: In this paper we introduce the notion of symmetric skew 3-derivations of prime or semiprime rings and prove that under certain conditions a prime ring with a nonzero symmetric skew 3-derivation has to be commutative.Found in: ključnih besedahSummary of found: ...symmetric skew 3-derivations of prime or semiprime rings and prove that under certain conditions a...Keywords: algebra, prime ring, semiprime ring, symmetric skew 3-derivation, centralizing mapping, commuting mappingPublished: 15.10.2013; Views: 1841; Downloads: 87 Full text (0,00 KB)
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