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Identities with generalized skew derivations on Lie ideals
Vincenzo De Filippis, Ajda Fošner, Feng Wei, 2013, izvirni znanstveni članek

Opis: 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 ▫$R$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: Zadetek v naslovu
Ključne besede: mathematics, algebra, polynomial identity, generalized skew derivation, prime ring
Objavljeno: 15.10.2013; Ogledov: 1755; Prenosov: 80
URL Polno besedilo (0,00 KB)

Decomposition of skew-morphisms of cyclic groups
István Kovács, Roman Nedela, 2011, izvirni znanstveni članek

Opis: A skew-morphism of a group ▫$H$▫ is a permutation ▫$\sigma$▫ of its elements fixing the identity such that for every ▫$x, y \in H$▫ there exists an integer ▫$k$▫ such that ▫$\sigma (xy) = \sigma (x)\sigma k(y)$▫. It follows that group automorphisms are particular skew-morphisms. Skew-morphisms appear naturally in investigations of maps on surfaces with high degree of symmetry, namely, they are closely related to regular Cayley maps and to regular embeddings of the complete bipartite graphs. The aim of this paper is to investigate skew-morphisms of cyclic groups in the context of the associated Schur rings. We prove the following decomposition theorem about skew-morphisms of cyclic groups ▫$\mathbb Z_n$▫: if ▫$n = n_{1}n_{2}$▫ such that ▫$(n_{1}n_{2}) = 1$▫, and ▫$(n_{1}, \varphi (n_{2})) = (\varphi (n_{1}), n_{2}) = 1$▫ (▫$\varphi$▫ denotes Euler's function) then all skew-morphisms ▫$\sigma$▫ of ▫$\mathbb Z_n$▫ are obtained as ▫$\sigma = \sigma_1 \times \sigma_2$▫, where ▫$\sigma_i$▫ are skew-morphisms of ▫$\mathbb Z_{n_i}, \; i = 1, 2$▫. As a consequence we obtain the following result: All skew-morphisms of ▫$\mathbb Z_n$▫ are automorphisms of ▫$\mathbb Z_n$▫ if and only if ▫$n = 4$▫ or ▫$(n, \varphi(n)) = 1$▫.
Najdeno v: ključnih besedah
Povzetek najdenega: Zadetek v naslovu
Ključne besede: cyclic group, permutation group, skew-morphism, Schur ring
Objavljeno: 15.10.2013; Ogledov: 1961; Prenosov: 58
URL Polno besedilo (0,00 KB)

Prime and semiprime rings with symmetric skew 3-derivations
Ajda Fošner, 2013, izvirni znanstveni članek

Opis: 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.
Najdeno v: ključnih besedah
Povzetek najdenega: Zadetek v naslovu
Ključne besede: algebra, prime ring, semiprime ring, symmetric skew 3-derivation, centralizing mapping, commuting mapping
Objavljeno: 15.10.2013; Ogledov: 1628; Prenosov: 76
URL Polno besedilo (0,00 KB)

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