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令A与B是含单位元的环,M是(A,B)-双模,U=Tri(A,M,B)是三角环.在一些附加假设条件下,本文从几个不同的角度给出了U上可加左导子的结构性质.此外,也得到了满足一定条件的环上可加左导子的两个不同刻画. 相似文献
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In this article, we examine algebras with a locally nilpotent q-skew σ-derivation d when there is an element x such that d(x) = 1 and either q is not a root of 1 or q = 1 in characteristic zero. When characteristic p > 0, we also examine the situation where d is an ordinary derivation. 相似文献
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Xiaofei Qi 《代数通讯》2013,41(10):3824-3835
Let ? be a unital prime ring with characteristic not 2 and containing a nontrivial idempotent P. It is shown that, under some mild conditions, an additive map L on ? satisfies L([A, B]) = [L(A), B] + [A, L(B)] whenever AB = 0 (resp., AB = P) if and only if it has the form L(A) = ?(A) + h(A) for all A ∈ ?, where ? is an additive derivation on ? and h is an additive map into its center. 相似文献
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Mohammad Ashraf Nadeem-ur-Rehman Shakir Ali 《Southeast Asian Bulletin of Mathematics》2002,25(3):379-382
Let R be a prime ring with characteristic different from two and U be a Lie ideal of R such that u2 U for all u U. In the present paper it is shown that if d is an additive mappings of R into itself satisfying d(u2) = 2ud(u), for all u U, then either U Z(R) or d(U) = (0).1991 Mathematics Subject Classification 16W25 16N60 相似文献
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Charles Lanski 《代数通讯》2013,41(11):3660-3672
We prove that a Jordan (φ, θ)-derivation of a 2-torsion free semiprime ring, with θ an automorphism, must be a (φ, θ)-derivation. This is then used to show more generally that an additive mapping of a semiprime ring to itself that behaves like a generalized (φ, θ)-derivation on nth powers is, in fact, a generalized (φ, θ)-derivation of the ring. 相似文献
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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
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Piotr Je¸drzejewicz 《代数通讯》2013,41(4):1500-1508
Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing Ap. 相似文献
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M. I. Gil' 《Mathematische Nachrichten》2002,244(1):78-88
Hille–Tamarkin matrices are investigated.Invertibility conditions and estimates for the norm of the inverse matrices are established. In addition, bounds for the spectrum are suggested. In particular, new estimates for the spectral radius are derived. 相似文献
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We show that if R is an infinite ring such that XY ∩ YX ≠ ? for all infinite subsets X and Y, then R is commutative. We also prove that in an infinite ring R, an element a ∈ R is central if and only if aX ∩ Xa ≠ ? for all infinite subsets X. 相似文献