1. Identities with generalized skew derivations on Lie idealsVincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, original scientific article Abstract: Let ▫$m, n$▫ be two nonzero fixed positive integers, ▫$R$▫ a 2torsion free prime ring with the right Martindale quotient ring ▫$Q$▫, ▫$L$▫ a noncentral 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 besedah Summary of found: ...fixed positive integers, ▫$R$▫ a 2torsion free prime ring with the right Martindale quotient ring... Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring Published: 15.10.2013; Views: 1931; Downloads: 90 Full text (0,00 KB) 
2. Jordan [tau]derivations of locally matrix ringsChenLian Chuang, Ajda Fošner, Tsiu Kwen Lee, 2013, original scientific article Abstract: 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 antiautomorphism 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 besedah Summary of found: ...Let ▫$R$▫ be a prime, locally matrix ring of characteristic not 2... Keywords: mathematics, algebra, antiautomorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫derivation, Banach space Published: 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 article Abstract: 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 twosided centralizer. Found in: ključnih besedah Summary 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 centralizer Published: 15.10.2013; Views: 1736; Downloads: 93 Full text (0,00 KB) This document has more files! More...

4. 