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101.
R是半素环,d是R的微商,ρ是R的右理想,a是R中元素,如果对于ρ中的所有元素x,都有ad(x)n=0,其中n是一个固定的正整数,那么必有aρd(P)P=0. 相似文献
102.
考虑具有导子的李三系.由李三系和一个导子称为LietsDer对.定义系数在表示中的LietsDer对的上同调理论.研究LietsDer对的中心扩张.接下来,将形变理论推广到由李三系和导子构成LietsDer对上,它由带有系数的LietsDer对的上同调所支配. 相似文献
103.
Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x1,…, xn) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) ? f(r)G(f(r))) = 0 for all r = (r1,…, rn) ∈ Rn, then one of the following holds:
There exist a, p, q, c ∈ U and λ ∈C such that F(x) = ax + xp + λx, G(x) = px + xq and d(x) = [c, x] for all x ∈ R, with [c, a ? q] = 0 and f(x1,…, xn)2 is central valued on R;
There exists a ∈ U such that F(x) = xa and G(x) = ax for all x ∈ R;
There exist a, b, c ∈ U and λ ∈C such that F(x) = λx + xa ? bx, G(x) = ax + xb and d(x) = [c, x] for all x ∈ R, with b + αc ∈ C for some α ∈C;
R satisfies s4 and there exist a, b ∈ U and λ ∈C such that F(x) = λx + xa ? bx and G(x) = ax + xb for all x ∈ R;
There exist a′, b, c ∈ U and δ a derivation of R such that F(x) = a′x + xb ? δ(x), G(x) = bx + δ(x) and d(x) = [c, x] for all x ∈ R, with [c, a′] = 0 and f(x1,…, xn)2 is central valued on R.
104.
Surjeet Kour 《代数通讯》2013,41(11):4100-4110
It is shown that the derivation y r ? x + (xy s + g)? y , where 0 ≤ r < s are integers, is a simple derivation of k[x, y], the polynomial ring in two variables over a field k of characteristic zero. 相似文献
105.
Let R be a noncommutative prime ring, U be the left Utumi quotient ring of R, and k, m, n, r be fixed positive integers. If there exist a generalized derivation G and a derivation g (which is independent of G) of R such that [G(xm)xn + xng(xm), xr]k = 0, for all x ∈ R, then there exists a ∈ U such that G(x) = ax, for all x ∈ R. As a consequence of the result in the present article, one may obtain Theorem 1 in Demir and Argaç [10]. 相似文献
106.
Charles Lanski 《代数通讯》2013,41(1):139-152
It is known that for a nonzero derivation d of a prime ring R, if a nonzero ideal I of R satisfies the Engel-type identity [[…[[d(x k 0 ), x k 1 ], x k 2 ],…], x k n ], then R is commutative. Here we extend this result to a skew derivation of R for a Lie ideal I, which has an immediate corollary that replaces d by an automorphism of R. A related result in two variables is obtained for d a (θ, ?)-derivation. 相似文献
107.
Hung-Yuan Chen 《代数通讯》2013,41(10):3709-3721
Let R be a noncommutative prime ring with extended centroid C, and let D: R → R be a nonzero generalized derivation, f(X 1,…, X t ) a nonzero polynomial in noncommutative indeterminates X 1,…, X t over C with zero constant term, and k ≥ 1 a fixed integer. In this article, D and f(X 1,…, X t ) are characterized if the Engel identity is satisfied: [D(f(x 1,…, x t )), f(x 1,…, x t )] k = 0 for all x 1,…, x t ∈ R. 相似文献
108.
109.
110.
Let 𝒜 be a unital algebra and let ? be a unitary 𝒜-bimodule. We consider Jordan generalized derivations mapping from 𝒜 into ?. Our results on unitary algebras are applied to triangular algebras. In particular, we prove that any Jordan generalized derivation of a triangular algebra is a generalized derivation. 相似文献