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141.
Vincenzo De Filippis 《代数通讯》2013,41(7):3139-3152
Let ? be a prime ring of characteristic different from 2, 𝒬r the right Martindale quotient ring of ?, 𝒞 the extended centroid of ?, F, G two generalized skew derivations of ?, and k ≥ 1 be a fixed integer. If [F(r), r]kr ? r[G(r), r]k = 0 for all r ∈ ?, then there exist a ∈ 𝒬r and λ ∈ 𝒞 such that F(x) = xa and G(x) = (a + λ)x, for all x ∈ ?. 相似文献
142.
143.
We study automorphisms of the incidence algebra of a finite quasiordered set M. In particular, we describe explicitly the group of outer automorphisms and give a criterion for any automorphism of this algebra to be a product of an inner one and an automorphism of M, which corrects some results of Spiegel (2001). 相似文献
144.
The Bose–Mesner algebra of the association scheme of the ordinary n-gon has the following remarkable properties:
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(i) It has a P-polynomial structure with respect to every faithful basis element; and
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(ii) Any closed subset generated by a basis element has a P-polynomial structure with respect to this basis element.
145.
Let R be a prime ring with center Z, L a noncentral Lie ideal of R, and σ a nontrivial automorphism of R such that [u σ,u] n ∈ Z for all u ∈ L. If either char(R) > n or char(R) = 0, then R satisfies s 4, the standard identity in 4 variables. 相似文献
146.
Jui-Chi Chang 《代数通讯》2013,41(6):2241-2248
Let R be a prime ring with center Z and L a noncommutative Lie ideal of R. Suppose that f is a right generalized β-derivation of R associated with a β-derivation δ such that f(x) n ∈ Z for all x ∈ L, where n is a fixed positive integer. Then f = 0 unless dim C RC = 4. 相似文献
147.
Koji Nuida 《代数通讯》2013,41(7):2559-2595
In this article, we prove that any irreducible Coxeter group of infinite order, which is possibly of infinite rank, is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group W, the centralizers in W of the normal subgroups of W that are generated by involu-tions. As a consequence, the problem of deciding whether two general Coxeter groups are isomorphic is reduced to the case of irreducible ones. We also describe the automorphism group of a general Coxeter group in terms of those of its irreducible components. 相似文献
148.
Zhengxin Chen 《代数通讯》2013,41(2):738-769
Let L be a finite-dimensional complex simple Lie algebra, L ? be the ?-span of a Chevalley basis of L, and L R = R ?? L ? be a Chevalley algebra of type L over a commutative ring R with identity. Let ?(R) be the solvable subalgebra of L R spanned by the basis elements of the maximal toral subalgebra and the root vectors associated with positive roots. In this article, we prove that under some conditions for R, any automorphism of ?(R) is uniquely decomposed as a product of a graph automorphism, a diagonal automorphism and an inner automorphism, and any derivation of ?(R) is uniquely decomposed as a sum of an inner derivation induced by root vectors and a diagonal derivation. Correspondingly, the automorphism group and the derivation algebra of ?(R) are determined. 相似文献
149.
150.
We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields. 相似文献