共查询到19条相似文献,搜索用时 46 毫秒
1.
2.
3.
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
4.
本文主要讨论了半素环的微商满足某些分恒等式的问题,给出了如下结果:假设R是带有扩张形心C的素环,I为R的稠密单侧理想,d和g是R的微商,如果d(x)g(x)=g(x)d(x)对任意x∈I均成立,那么对第一个x∈R,d^2(x)=0,或者存在λx∈C使得d(x)-λxg(x)∈C,同时给出了半素环的微商满足某些微分恒等式的结果。 相似文献
5.
In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms. 相似文献
6.
8.
Let R be a prime ring of characteristic different from 2,d and g twoderivations of R at least one of which is nonzero,L a non-central Lie ideal of R,anda∈R.We prove that if a(d(u)u-ug(u))=0 for any u∈L,then either a=0,or R is an s_4-ring,d(x)=[p,x],and g(x)=-d(x)for some p in the Martindalequotient ring of R. 相似文献
9.
半素环的几个交换性条件 总被引:7,自引:0,他引:7
一个半素环 R是交换环当且仅当 R满足下列条件之一 :( ) (xmy) n+xmy∈ Z(R) ,对任意的 x ,y∈ R。( ) (xmy) n- yxm∈ Z(R) ,对任意的 x,y∈ R。( ) (xmy) n+yxm∈ Z(R) ,对任意的 x,y∈ R。其中 m,n是固定的正整数且 n >1 相似文献
10.
Let R be a prime ring with an automorphism σ≠1, an identity map. Let L be a noncentral Lie ideal of R such that [x^σ,x] E Z for all x ∈ L, where Z is the center of R. Then L is contained in the center of R, unless char(R)=2 and dimc RC = 4. 相似文献
11.
Cheng-Kai Liu 《代数通讯》2013,41(4):1747-1756
Let R be a 2-torsion free commutative ring with involution, and δ a nonzero derivation of R. Let S be the set of symmetric elements in R, and let K be the set of anti-symmetric elements in R. In this article, we investigate the semiprimeness of the Lie rings Sδ when δ is symmetric and Kδ when δ is anti-symmetric. 相似文献
12.
Throughout,R will be semiprime ring,Qmr=Qmr(R) the maximal right quotient ringof R,and C=Z(Qmr) the extended centroid of R(see[1 ,Chapter2 ] for details) . In [2 ] ,Bresar,M.discussed the identity of derivations in a prime ring,and provedthat if nonzero derivations d and g of R satisfy d(x) g(y) =g(x) d(y) for all x,y∈R,then there exists aλ in C such thatg(x) =λd(x) for all x∈ R.Itis natural to ask whatresults can be obtained if d(x) g(x) =g(x) d(x) for all x∈ R.In[3 ] ,Bresa… 相似文献
13.
Mikhail A. Chebotar 《代数通讯》2013,41(12):4339-4344
Let R be a 2-torsion free commutative ring with identity, and δ a nonzero derivation of R such that R is δ-prime. Then Rδ is a prime Lie ring and any nonzero ideal of Rδ contains an ideal of the form Jδ where J is a nonzero δ-ideal of R. 相似文献
14.
Generalized Derivations with Nilpotent Values on Semiprime Rings 总被引:1,自引:0,他引:1
FengWEI 《数学学报(英文版)》2004,20(3):453-462
Let R be a semiprime ring, RF be its left Martindale quotient ring and I be an essential ideal of R. Then every generalized derivation μ defined on I can be uniquely extended to a generalized derivation of RE. Furthermore, if there exists a fixed positive integer n such that μ(x)^n = 0 for all x∈I, then μ=0. 相似文献
15.
16.
Yen-Jen Chen 《代数通讯》2013,41(2):792-796
Let R be a semiprime ring with extended centroid C and with Q its Martindale symmetric ring of quotients. Suppose that δ: R → R is a C-integral derivation. For a subring A of Q, let A(δ) denote the subring of constants of δ in A. We prove that R(δ) and Q(δ) satisfy the same polynomial identities with coefficients in C. In particular, R(δ) is not nil of bounded index. 相似文献
17.
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
18.
N-Centralizing Mappings in Semiprime Rings 总被引:1,自引:0,他引:1
N┐CentralizingMappingsinSemiprimeRingsMajeed,A.H.andNiuFengwen(牛凤文)(DepartmentofMathematics,JilinUniversity,Changchun,130023)... 相似文献
19.
《代数通讯》2013,41(2):969-979
Abstract Let R be a prime ring of characteristic not equal to 2 or 3 and let L be a noncentral Lie ideal of R. Suppose that σ is a Lie automorphism on L such that σ4 is not the identity map. Then the additive subgroup generated by the set {[x σ, x] ∣ x ∈ L} contains a noncentral Lie ideal of R. 相似文献