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设R是一个素环,RF是它的左Martindale商环.如果φ(xigik△ij)是环R的某个本质理想I的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(zikj)是环RF的一个广义多项式恒等式.设R是一个具有特征P≥0的半素环,RF是它的左Martindale商环.如果φ(xigik△ijfik)是环R的一个多重线性既约且带有自同构的广义微分恒等式,那么φ(zikjfike(△ij)是环RF的一个广义多项式恒等式,这里fik和e(△ij)是RF中的幂等元. 相似文献
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罗朗级数环的主拟Baer性 总被引:3,自引:0,他引:3
称环 R为右主拟 Baer环(简称为右p·q.Baer环),如果 R的任意主右理想的右零化子可由幂等元生成.本文证明了,若环 R满足条件Sl(R)(?)C(R),则罗朗级数环R[[x,x-1]]是右p.q.Baer环当且仅当R是右p.q.Baer环且R的任意可数多个幂等元在I(R)中有广义join.同时还证明了,R是右p.q.Baer环当且仅当R[x,x-1]是右P.q.Baer环. 相似文献
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环R中元素a称为强拟诣零clean元,若存在幂等元e∈R和拟幂零元q∈R使得eq=qe且a=e+q;称环R为强拟诣零clean环,如果R中每一个元素均是强拟诣零clean元.强拟诣零clean环介于强诣零clean环和强clean环之间,并且每一个强拟诣零clean元是强clean元.本文介绍了强拟诣零clean环的基本性质和结构,并研究了局部环R上广义矩阵环K_s(R)的强拟诣零clean性. 相似文献
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J.A.Beachy 研究过 R-mod 上的极大的 Torsion 理论,(见[2])我们在这里讨论极大 Torsion 理论的忠实性。得到如下的结果:当 z(R)=0时,极大而且忠实的 Torsion理论仅有 Goldie Torsion 理论。设 R 是满足右零化子升链条件的结合环,τ是 R-mod上的一个极大的 Torsion 理论,那么τ是忠实的一个充分条件是 R 为素环。当 R 为半素环时,这个条件也是必要的。 相似文献
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游松发 《数学的实践与认识》2001,31(5):576-578
R是素 GPI-环 ,若多项式 f (x1,… ,xd)在 R上是幂零的 ,则或 f (x1,… ,xd)是 R的恒等式 ,或 R是有限域上的有限矩阵环 . 相似文献
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交换环R称为(受限制的)弱准素环,如果R中的每个(非零)主理想都是准素理想.本文证明了一个没有单位元的交换环R是受限制的弱准素环当且仅当R是每个元素都是幂零元的交换环或者R是仅含一个真素理想P的没有单位元的交换环并且P不真包含R的任何非零理想. 相似文献
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Let R be an(α,δ)-compatible ring.It is proved that R is a 2-primal ring if and only if for every minimal prime ideal P in R[x;α,δ] there exists a minimal prime ideal P in R such that P = P [x;α,δ],and that f(x) ∈ R[x;α,δ] is a unit if and only if its constant term is a unit and other coefficients are nilpotent. 相似文献
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Let Mbe a monoid. A ring Ris called M-π-Armendariz if whenever α = a1g1+ a2g2+ · · · + angn, β = b1h1+ b2h2+ · · · + bmhm ∈ R[M] satisfy αβ ∈ nil(R[M]), then aibj ∈ nil(R) for all i, j. A ring R is called weakly 2-primal if the set of nilpotent elements in R coincides with its Levitzki radical. In this paper, we consider some extensions of M-π-Armendariz rings and further investigate their properties under the condition that R is weakly 2-primal. We prove that if R is an M-π-Armendariz ring then nil(R[M]) = nil(R)[M]. Moreover, we study the relationship between the weak zip-property (resp., weak APP-property, nilpotent p.p.-property, weak associated prime property) of a ring R and that of the monoid ring R[M] in case R is M-π-Armendariz. 相似文献
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Firstly,the commutativity of rings is investigated in this paper.Let R be a ring with identity.Then we obtain the following commutativity conditions: (1) if for each x ∈ R\N(R) and each y ∈ R,(xy)k =xkyk for k =m,m + 1,n,n + 1,where m and n are relatively prime positive integers,then R is commutative;(2) if for each x ∈ R\J(R) and each y ∈ R,(xy)k =ykxk for k =m,m+ 1,m+2,where m is a positive integer,then R is commutative.Secondly,generalized 2-CN rings,a kind of ring being commutative to some extent,are investigated.Some relations between generalized 2-CN rings and other kinds of rings,such as reduced rings,regular rings,2-good rings,and weakly Abel rings,are presented. 相似文献
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J-semicommutative环的性质 总被引:1,自引:0,他引:1
环冗称为J—semicommutative若对任意B,b∈R由ab=0可以推得aRb∈J(R),这里J(R)是环R的Jacobson根.环R是J—semicommutative环当且仅当它的平凡扩张是J—semicommutative环当且仅当它的Don'oh扩张是J—semicommutative环当且仅当它的Nagata扩张是,一semicommutative环当且仅当它的幂级数环是J—semicommutative环.若R/J(R)是semicommutative环,则可得到R是J-semicommutative环.本文进一步论证了如果,是环月的一个幂零理想,且R/I是J—semicommutative环,则R也是J-semicommutative环最后给出了J—semicommutative环与其他一些常见环的联系 相似文献
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Let α be a nonzero endomorphism of a ring R, n be a positive integer and T_n(R, α) be the skew triangular matrix ring. We show that some properties related to nilpotent elements of R are inherited by T_n(R, α). Meanwhile, we determine the strongly prime radical, generalized prime radical and Behrens radical of the ring R[x; α]/(x~n), where R[x; α] is the skew polynomial ring. 相似文献
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对于给定的正整数k≥1,环R上的元x,y的k-Jordan乘积定义为{x,y}_k={{x,y}_(k-1),y}_1,其中{x,y}_0=x,{x,y}_1=xy+yx.假设R是包含有单位元与一非平凡幂等元的素环.本文证明了R上的满射f满足{f(x),f(y)}2={x,y}_2对所有x,y∈R成立当且仅当存在λ∈l(R的可扩展中心)且λ~3=1,使得下列之一成立:(1)若R的特征不为2,则f(x)=λx对所有x∈R成立;(2)若R的特征为2,则f(x)=λx+μ(x)对所有x∈R成立,其中μ:R→l是一个映射.作为应用,得到了因子von Neumann代数上保持上述性质映射的结构. 相似文献
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设R是素环,I是R的非零理想,如果R容许一个非单位映射的左乘子使得对所有x,y∈I满足δ(x°y)=x°y或δ(x°y) x°y=0,那么R可交换.此外,如果R是2-扭自由的素环,U是平方封闭的李理想,γ是伴随导子非零的广义导子,B:R×R→R是迹函数为g(x)=B(x,x)的对称双导,当下列条件之一成立时U为中心李理想(1)γ同态作用于U(2)2[x,y]-g(xy) g(yx)∈Z(R)(3)2[x,y] g(xy)-g(yx)∈Z(R)(4)2(x°y)=g(x)-g(y)(5)2(x°y)=g(y)-g(x)对所有的x,y∈U. 相似文献
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In 1999,Kim and Kwak asked one question that "Is a ring R 2-primal if OP■P for each P ∈ mSpec(R)?".In this paper,we prove that if O P has the IFP for each P ∈ mSpec(N),then OP■P for each P ∈ mSpec(N) if and only if N is a 2-primal near-ring and also we give characterization of 2-primal near-rings by using its minimal 0-prime ideals. 相似文献
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G. V. Dorofeev 《Mathematical Notes》1976,19(2):172-175
It is proved that the identities ([x, y]4, z, t) = ([x, y]2, z, t) [x, y] = [x, y] ([x, y]2, z, t) = 0, known in the theory of alternative rings as the Kleinfeld identities, are fulfilled in every generalized accessible ring of characteristic different from 2 and 3. These identities allow us to construct central and kernel functions in the variety of generalized accessible rings. It is also proved that in a free generalized accessible and a free alternative ring with more than three generators the Kleinfeld element ([x, y]2, z, t) is nilpotent of index 2.Translated from Matematicheskie Zametki, Vol. 19, No. 2, pp. 291–297, February, 1976. 相似文献