共查询到20条相似文献,搜索用时 10 毫秒
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Let R be a ring. A map ${F : R \rightarrow R}$ F : R → R is called a multiplicative (generalized)-derivation if F(xy) = F(x)y + xg(y) is fulfilled for all ${x, y \in R}$ x , y ∈ R where ${g : R \rightarrow R}$ g : R → R is any map (not necessarily derivation). The main objective of the present paper is to study the following situations: (i) ${F(xy) \pm xy \in Z}$ F ( xy ) ± xy ∈ Z , (ii) ${F(xy) \pm yx \in Z}$ F ( xy ) ± yx ∈ Z , (iii) ${F(x)F(y) \pm xy \in Z}$ F ( x ) F ( y ) ± xy ∈ Z and (iv) ${F(x)F(y) \pm yx \in Z}$ F ( x ) F ( y ) ± yx ∈ Z for all x, y in some appropriate subset of R. Moreover, some examples are also given. 相似文献
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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
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A. A. Tuganbaev 《Mathematical Notes》1995,58(5):1197-1215
It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx
n
A=Ax
n
. We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive
left Noetherian PI rings. We also characterize rings all of whose Pierce stalks are right chain right Artin rings.
Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 736–761, November, 1995. 相似文献
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J. V. Kochetova 《Journal of Mathematical Sciences》2010,164(2):245-249
The concepts of prime Lie algebras and semiprime Lie algebras are important in the study of Lie algebras. The purpose of this
paper is to investigate generalizations of these concepts to lattice ordered Lie algebras over partially ordered fields. Some
results concerning the properties of l-prime and l-semiprime lattice ordered Lie algebras are obtained. A necessary and sufficient condition for a lattice ordered Lie algebra
to be an l-prime Lie l-algebra is presented. 相似文献
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Differential identities of semiprime rings 总被引:9,自引:0,他引:9
V. K. Kharchenko 《Algebra and Logic》1979,18(1):58-80
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LetR be a ring and σ an automorphism ofR. We prove the following results: (i)J(R
σ[x])={Σiri
x
i:r0∈I∩J(R]),
r
i∈I for alliε 1} whereI↪ {r∈R:rx ∈J(R
Σ[x])|s= (ii)J(R
σ<x>)=(J(R
σ<x>)∩R)σ<x>. As an application of the second result we prove that ifG is a solvable group such thatG andR, + have disjoint torsions thenJ(R)=0 impliesJ(R(G))=0. 相似文献
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Shuliang Huang 《Czechoslovak Mathematical Journal》2011,61(4):1135-1140
Let R be a prime ring, I a nonzero ideal of R, d a derivation of R and m, n fixed positive integers. (i) If (d[x, y])
m
= [x, y]
n
for all x, y ∈ I, then R is commutative. (ii) If Char R ≠ 2 and [d(x), d(y)]
m
= [x, y]
n
for all x, y ∈ I, then R is commutative. Moreover, we also examine the case when R is a semiprime ring. 相似文献