共查询到20条相似文献，搜索用时 21 毫秒
1.
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
2.
If k is a field of characteristic zero, c ∈ k?0, and 1 ≤ s ≤ r are integers such that either r ? s + 1 divides s or s divides r ? s + 1, then it is shown that the derivation y r ? x + (xy s + c)? y of the polynomial ring k[x, y] is simple. 相似文献
3.
M'hammed El Kahoui 《Proceedings of the American Mathematical Society》2004,132(9):2537-2541
A well-known theorem, due to Nagata and Nowicki, states that the ring of constants of any -derivation of , where is a commutative field of characteristic zero, is a polynomial ring in one variable over . In this paper we give an elementary proof of this theorem and show that it remains true if we replace by any unique factorization domain of characteristic zero.
4.
Let K be a commutative ring with unity, R a prime K-algebra, Z(R) the center of R, d and δ nonzero derivations of R, and f(x 1,…, x n ) a multilinear polynomial over K. If [d(f(r 1,…, r n )), δ (f(r 1,…, r n ))] ? Z(R), for all r 1,…, r n ? R, then either f(x 1,…, x n ) is central valued on R or {d, δ} are linearly dependent over C, the extended centroid of R, except when char(R) = 2 and dim C RC = 4. 相似文献
5.
On approximately higher ring derivations 总被引：1，自引：0，他引：1
In this paper, we examine the Hyers-Ulam, the Isac and Rassias-type stability and the Bourgin-type superstability of a functional inequality corresponding to the following functional equation, respectively:
6.
Jason McGraw 《代数通讯》2013,41(3):947-954
In this article, we describe all gradings by finite groups on the Witt algebra over an algebraically closed field of characteristic greater than 3. 相似文献
7.
Yuan-Tsung Tsai 《代数通讯》2013,41(10):3608-3615
Let R be a domain and R[X; D] the Ore extension of R by a sequence D of derivations of R. If D has length ≥ 2, we show that the symmetric Utumi quotient ring of R[X; D] is U s (R)[X; D], where U s (R) is the symmetric Utumi quotient ring of R. Consequently, X-inner automorphisms of R[X; D] are induced by units of U s (R) and the extended centroid of R[X; D] consists of those elements α in the center of U s (R) such that δ(α) = 0 for all δ ? D. These extend the known results for free algebras. 相似文献
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10.
This paper abstracts some results of M. Bresar and J. Vukman [1] on the orthogonal derivations of semiprime rings to (σ, τ)-derivations and generalized (σ, τ)-derivations. 相似文献
11.
V. V. Bavula 《Transactions of the American Mathematical Society》2008,360(8):4007-4027
Let be a differentiably simple Noetherian commutative ring of characteristic (then is local with ). A short proof is given of the Theorem of Harper (1961) on classification of differentiably simple Noetherian commutative rings in prime characteristic. The main result of the paper is that there exists a nilpotent simple derivation of the ring such that if , then for some . The derivation is given explicitly, and it is unique up to the action of the group of ring automorphisms of . Let be the set of all such derivations. Then . The proof is based on existence and uniqueness of an iterative -descent (for each ), i.e., a sequence in such that , and for all . For each , and .
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13.
A. Firat 《Siberian Mathematical Journal》2006,47(1):169-172
Given a prime ring R, a skew g-derivation for g : R → R is an additive map f : R → R such that f(xy) = f(x)g(y) + xf(y) = f(x)y + g(x)f(y) and f(g(x)) = g(f(x)) for all x, y ∈ R. We generalize some properties of prime rings with derivations to the class of prime rings with skew derivations. 相似文献
14.
Tsiu-Kwen Lee 《代数通讯》2017,45(7):2967-2968
We give a short proof of Litoff’s theorem from the viewpoint of completely reducible modules. 相似文献
15.
Let K be a commutative ring with unity, R a prime K-algebra of characteristic different from 2, U the right Utumi quotient ring of R, f(x 1,…, x n ) a noncentral multilinear polynomial over K, and G a nonzero generalized derivation of R. Denote f(R) the set of all evaluations of the polynomial f(x 1,…, x n ) in R. If [G(u)u, G(v)v] = 0, for any u, v ∈ f(R), we prove that there exists c ∈ U such that G(x) = cx, for all x ∈ R and one of the following holds: 1. f(x 1,…, x n )2 is central valued on R; 2. R satisfies s 4, the standard identity of degree 4. 相似文献
16.
Bruno Leonardo Macedo Ferreira Henrique Guzzo Jr. Ruth Nascimento Ferreira Feng Wei 《代数通讯》2020,48(2):717-723
17.
Let R be a prime ring, with no nonzero nil right ideal, Q the two-sided Martindale quotient ring of R, F a generalized derivation of R, L a noncommutative Lie ideal of R, and b ∈ Q. If, for any u, w ∈ L, there exists n = n(u, w) ≥1 such that (F(uw) ? bwu)n = 0, then one of the following statements holds:
F = 0 and b = 0;
R ? M2(K), the ring of 2 × 2 matrices over a field K, b2 = 0, and F(x) = ?bx, for all x ∈ R.
18.
Mohammad Ashraf Vincenzo De Filippis Sajad Ahmad Pary Shailesh Kumar Tiwari 《代数通讯》2019,47(2):800-813
19.
Let R be a prime ring with center Z and S (?) R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x-xG(x) ∈ Z for all x ∈ S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime case is also considered. 相似文献
