共查询到19条相似文献,搜索用时 62 毫秒
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满足R—左模同态链归纳条件之环 总被引:2,自引:0,他引:2
环的链条件已得到深入的研究,其成果相当丰富。许永华曾提出过一种新的链条件,即R—左模同态链归纳条件。此条件完全脱离了以往的链条件的有限性,且是著名的Kthe猜测成立的充分必要条件。本文的目的是要指出:此条件不仅能使Kthe猜想成立,而且还可以得出另一些有意义的结果。我们引进了一个环的Levitzki子集的概念。从而证明了:环R的Levitzki根包含R的任何诣零单侧理想的充分必要条件是R满足每个Levitzki子集上R—左模同态链归纳条件。 本文同时还讨论了Kegel猜测:环R的两个局部幂零子环之和仍为局部幂零的。我们得到的结果是:如果环R=A B,A为R的诣零左理想,B为R的谐零子环,则R是局部幂零的。当且仅当R满足R-L(R)的每一子集上R-左模同态链归纳条件。此处L(R)为R的Levitzki根。 本文所讨论的环都是结合环(不要求有单位元)。没有给出明确定义的术语其意义与[1]相同。 相似文献
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如果R中每个元素(对应地,可逆元)均可表示为一个幂等元与环R的Jacobson根中一个元素之和,则称环R是J-clean环(对应地,UJ环).所有的J-clean环都是UJ环.作为UJ环的真推广,本文引入GUJ环的概念,研究GUJ环的基本性质和应用.进一步地,研究每个元素均可表示为一个幂等元与一个方幂属于环的Jacobson根的元素之和的环. 相似文献
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本文称环Ω的左(右)理想A为因子幂零的,如果对于任意元素r∈Ω,均有正整数m=m(r),使得Amr={0}.称Ω的一个左理想L为关于元素b∈Ω的左因子,如果Lb≠{0}.定理4 设R是环Ω的因子幂零右理想,那么R+ΩR是Ω的一个因子幂零理想.定理7 设Ω具有局部左因子极小条件,那么Ω的任意诣零左理想必是因子幂零左理想.本文指出因子幂零性是介于幂零性与诣零性之间的一种性质,更接近幂零性。 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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称环R为广义2-素环,如果R的幂零元集与上诣零根一致.证明了R上的多项式为单位当且仅当它的常数项是R中的单位而其它系数是幂零的.因此,广义2-素环上的多项式环的稳定度大于一. 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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Czechoslovak Mathematical Journal - Let k be a field of characteristic zero and B a k-domain. Let R be a retract of B being the kernel of a locally nilpotent derivation of B. We show that if B = R... 相似文献
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P. Shumyatsky’s question 11.126 in the “Kourovka Notebook” is answered in the affirmative: it is proved that there exist a
constant c and a function of a positive integer argument f(m) such that if a finite group G admits an automorphism ϕ of order
4 having exactly m fixed points, then G has a normal series G ⩾ H ⩽ N such that |G/H| ⩽ f(m), the quotient group H/N is nilpotent
of class ⩽ 2, and the subgroup N is nilpotent of class ⩽ c (Thm. 1). As a corollary we show that if a locally finite group
G contains an element of order 4 with finite centralizer of order m, then G has the same kind of a series as in Theorem 1.
Theorem 1 generalizes Kovács’ theorem on locally finite groups with a regular automorphism of order 4, whereby such groups
are center-by-metabelian. Earlier, the first author proved that a finite 2-group with an almost regular automorphism of order
4 is almost center-by-metabelian. The proof of Theorem 1 is based on the authors’ previous works dealing in Lie rings with
an almost regular automorphism of order 4. Reduction to nilpotent groups is carried out by using Hall-Higman type theorems.
The proof also uses Theorem 2, which is of independent interest, stating that if a finite group S contains a nilpotent subgroup
T of class c and index |S: T | = n, then S contains also a characteristic nilpotent subgroup of class ⩽ c whose index is bounded
in terms of n and c. Previously, such an assertion has been known for Abelian subgroups, that is, for c = 1.
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Translated from Algebra i Logika, Vol. 45, No. 5, pp. 575–602, September–October, 2006. 相似文献
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We study locally nilpotent groups containing subgroups of classc, c>1, and satisfying the weak maximum condition or the weak minimum condition on c-nilpotent subgroups. It is proved that nilpotent groups of this type are minimax and periodic locally nilpotent groups of this type are Chernikov groups. It is also proved that if a group G is either nilpotent or periodic locally nilpotent and if all of its c-nilpotent subgroups are of finite rank, then G is of finite rank. If G is a non-periodic locally nilpotent group, these results, in general, are not valid.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 384–389, March, 1992. 相似文献
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Emanuel Kolb 《Results in Mathematics》1992,21(3-4):345-354
It is shown that every non-trivial norm on a nearfield F induces a topology T on F such that (F,T) is a locally bounded semitopological nearring with nonzero topological nilpotent elements and that any such topology can be obtained by a non-trivial norm. 相似文献
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Let R be an associative ring with identity.R is said to be semilocal if R/J(R)is(semisimple)Artinian,where J(R)denotes the Jacobson radical of R.In this paper,we give necessary and sufficient conditions for the group ring RG to be semilocal,where G is a locally finite nilpotent group. 相似文献
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L. A. Kurdachenko 《Ukrainian Mathematical Journal》1990,42(3):303-307
The study of locally nilpotent groups with the weak minimality condition for normal subgroups, the min––n condition, is continued. The following results are obtained.THEOREM 1. A locally nilpotent group with the min––n condition is countable.THEOREM 2. If G is a locally nilpotent group with the min––n condition whose periodic part is nilpotent and the orders of the elements of the periodic part are bounded in the aggregate, then G=t(G)A, where the subgroup A is minimax.THEOREM 3. Suppose G is a locally nilpotent group with the min––n condition and T is its periodic part. If T is nilpotent and G/T is Abelian, then G=TA, where the subgroup A is minimax.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 340–346, March, 1990. 相似文献
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In 1992, Wilson and Zelmanov proved that a profinite Engel group is locally nilpotent. Here we prove the stronger result that
every compact Engel group is locally nilpotent. 相似文献
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A. M. Slin'ko 《Mathematical Notes》1974,16(1):664-667
Subject to a certain restriction on the additive group of an alternative ring A, we prove that R(A)=R(A(+)), where A(+) is a Jordan ring and R is one of the following radicals: the Jacobson radical, the upper nil-radical, the locally nilpotent radical, or the lower nil-radical. For the proof of these relationships Herstein's well-known construction for associative rings is generalized to alternative rings. 相似文献
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Andreas J. Guelzow 《组合设计杂志》1993,1(4):301-321
Steiner quadruple systems can be coordinatized by SQS-skeins. We investigate those Steiner quadruple systems that correspond to finite nilpotent SQS-skeins. S. Klossek has given representation and construction theorems for finite distributive squags and Hall triple systems which were generalized by the author to the class of all finite nilpotent squags and their corresponding Steiner triple systems. In this article we present analogous theorems for nilpotent SQS-skeins and Steiner quadruple systems. We also generalize the well-known doubling constructions of Doyen/Vandensavel and Armanious. It is then possible to describe the structure of all nilpotent Steiner quadruple systems completely: the nilpotent Steiner quadruple systems are exactly those obtained from the trivial 2- (or 4-) element Steiner quadruple system by repeated application of this generalized doubling construction. Moreover, we prove that the variety of semi-boolean SQS-skeins is not locally finite and contains non-nilpotent SQS-skeins. © 1993 John Wiley & Sons, Inc. 相似文献