1. The Hyers-Ulam-Rassias stability of (m,n)[sub]{([sigma], [tau])}-derivations on normed algebrasAjda Fošner, 2012, original scientific article Abstract: We study the Hyers-Ulam-Rassias stability of ▫$(m,n)_{(\sigma,\tau)}$▫-derivations on normed algebras. Found in: ključnih besedah Summary of found: ...... Keywords: Hyers-Ulam-Rassias stability, normed algebra, ▫$(m, n)_{(\sigma, \tau)}$▫-derivation Published: 15.10.2013; Views: 1192; Downloads: 14 Full text (0,00 KB) |
2. 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 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 besedah Summary of found: ...... Keywords: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring Published: 15.10.2013; Views: 1619; Downloads: 72 Full text (0,00 KB) |
3. On generalized Jordan triple ([alpha], [beta]) [sup] [ast]-derivations and related mappingsShakir Ali, Ajda Fošner, Maja Fošner, Mohammad Salahuddin Khan, 2013, original scientific article Abstract: Let ▫$R$▫ be a 2-torsion free semiprime ▫$\ast$▫-ring and let ▫$\alpha, \beta$▫ be surjective endomorphisms of ▫$R$▫. The aim of the paper is to show that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on ▫$R$▫ is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. This result makes it possible to prove that every generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation on a semisimple ▫$H^\ast$▫-algebra is a generalized Jordan ▫$(\alpha, \beta)^\ast$▫-derivation. Finally, we prove that every Jordan triple left ▫$\alpha^\ast$▫-centralizer on a 2-torsion free semiprime ring is a Jordan left ▫$\alpha^\ast$▫-centralizer. Found in: ključnih besedah Summary of found: ...... Keywords: mathematics, algebra, semiprime ▫$\ast$▫-ring, ▫$H^\ast$▫-algebra, Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, generalized Jordan triple ▫$(\alpha, \beta)^\ast$▫-derivation, Jordan triple left ▫$\alpha^\ast$▫-centralizer Published: 15.10.2013; Views: 1500; Downloads: 24 Full text (0,00 KB) |
4. Jordan [tau]-derivations of locally matrix ringsChen-Lian 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 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 besedah Summary of found: ...... Keywords: mathematics, algebra, anti-automorphism, locally matrix ring, prime ring, Jordan homomorphism, Jordan ▫$\tau$▫-derivation, Banach space Published: 15.10.2013; Views: 1490; Downloads: 22 Full text (0,00 KB) |
5. On the generalized Hyers-Ulam stability of module left (m, n)-derivationsAjda Fošner, 2012, original scientific article Abstract: We study the generalized Hyers-Ulam stability of functional equations of module left ▫$(m, n)$▫-derivations. Found in: ključnih besedah Summary of found: ...... Keywords: mathematics, algebra, generalized Hyers-Ulam stability, normed algebra, Banach left A-module, module left ▫$(m, n)$▫-derivation Published: 15.10.2013; Views: 1807; Downloads: 60 Full text (0,00 KB) |
6. Hyers-Ulam-Rassias stability of generalized module left (m,n)-derivationsAjda Fošner, 2013, original scientific article Abstract: The generalized Hyers-Ulam-Rassias stability of generalized module left ▫$(m,n)$▫-derivations on a normed algebra ▫$\mathcal{A}$▫ into a Banach left ▫$\mathcal{A}$▫-module is established. Found in: ključnih besedah Summary of found: ...normed algebra, Banach left A-module, module left (m,n)-derivation, generalized module left (m,n)-derivation... Keywords: Hyers-Ulam-Rassias stability, normed algebra, Banach left A-module, module left (m, n)-derivation, generalized module left (m, n)-derivation Published: 15.10.2013; Views: 1622; Downloads: 42 Full text (0,00 KB) |
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