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《Quaestiones Mathematicae》2013,36(3):403-416
Abstract Dedicated to the memory of John Knopfmacher (1937–1999) We describe the q-Engel series expansion for Laurent series discovered by John Knopfmacher and use this algorithm to shed new light on partition identities related to two entries from Slater's list. In our study Al-Salam/Ismail and Santos polynomials play a crucial r?ole. 相似文献
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作为-/R^n上的离散收敛群中的初等群的推广,本文定义了-/R^n上一般收敛群中的初等群和拟初等群,并得到了初等收敛群、拟初等收敛群和非拟初等敛群各自的一些性质和特征。 相似文献
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<正> 在[1]中,作者研究了一个(N—1)维连通空间的同伦群和同调群的密切关系,那里所考虑的同伦群的维数是在(2N—2)以内,本文可以看成[1]的继续,我偿将考虑维数在(2N—1)以上而又在(3N—3)以下的同伦群,Betti 数;和上乘积的密切关系.我们 相似文献
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《代数通讯》2013,41(9):4527-4547
ABSTRACT This paper is devoted to present, first, a family of formulas extending to the multivariate case the classical Newton (or Newton–Girard) Identities relating the coefficients of a univariate polynomial equation with its roots through the Newton Sums and, secondly, the Generating Functions associated to the new introduced Newton Sums of the multivariate case. As a by-product the kinds of systems accepting these Newton Identities are also characterized together with those allowing the Newton Sums to be computed in an inductive way directly from the coefficients of the polynomial system under consideration. 相似文献
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对上式利用对角线相消法则得(2).证毕.注意到定义(1)可以视为普通升降乘和 q 升阶乘算子的概括和拓广.因此可以期望由部分和公式(2)得到部分关于二项式系数和 Gauss 二项式系数的卷积型组合恒等式.下面便进行这方面的讨论. 相似文献
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Euler数与Bernoulli数的一些恒等式 总被引:2,自引:0,他引:2
陈志明 《纯粹数学与应用数学》1994,10(1):7-10
本文的主要目的是利用初等方法给出Euler数与Bernoulli数的一些有关恒等式。 相似文献
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《代数通讯》2013,41(9):3787-3800
Let A be a superalgebra over a field of characteristic zero. In this paper we investigate the graded polynomial identities of A through the asymptotic behavior of a numerical sequence called the sequence of graded codimensions of A. Our main result says that such sequence is polynomially bounded if and only if the variety of superalgebras generated by A does not contain a list of five superalgebras consisting of a 2-dimensional algebra, the infinite dimensional Grassmann algebra and the algebra of 2 × 2 upper triangular matrices with trivial and nontrivial gradings. Our main tool is the representation theory of the symmetric group. 相似文献
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本文研究了Chebyshef多项式的一类幂和问题.利用初等方法以及Chebyshef多项式的性质,获得了一些有趣的恒等式,推广了Melham关于Lucas数的奇数次幂和的猜想. 相似文献
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《Quaestiones Mathematicae》2013,36(1-3):143-155
We study the question of what properties of nilpotent groups are shared by their abelianizations. We identify two such properties—that of being a π-torsion group, where π is a family of primes, and that of having qth roots, for some prime q. We use these properties to provide simplified proofs of the following theorems in the localization of nilpotent groups. Let H, K be subgroups of the nilpotent group N and let P be a family of primes. Then [H, K] P = [HP, Kp] Let the group G act on the nilpotent group N. Then G acts compatibly on Np and (ΓG i N)P = ΓG i(Np). The second theorem above is then applied to the study of the localization of relative groups, in the sense of [4]. 相似文献
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《代数通讯》2013,41(2):935-969
ABSTRACT The concepts of the fractional and the strong degree of an element in a ring are introduced. It is shown that definitive results on functional identities can be obtained in rings which contain elements of appropriate fractional (or strong) degree. This enables us to extend the results on functional identities from prime to semiprime rings, as well as to some rather different classes of rings, such as matrix rings over any unital ring. As an application, commuting maps, Lie derivations and commutativity preserving maps in such rings are discussed. 相似文献
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<正> 最近几年来,关于同伦群的研究,特别是球面同化群的计算有很大的进步,但是关于更一般的空间的同伦群的计算,就作者所知道的文献来说,似乎没有相应的进展,在这一方面的工作,最早也是最主要的是 Hurewicz 定理,Serre 在[15]中利用所谓 C同构的概念,把 Hurewicz 定理推广到所谓(n-1)维 C 连通空间中,但是也和 Hure-wicz 定理一样,只能讨论 n 维同伦群和 n 维同调群的关系.张素诚,Hilton 及 Barrat 相似文献
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A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions. 相似文献
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本文研究了泛欧氏空间的Clifford群、扭群、旋群,它们为Clifford代数中选出极好的一类子群.利用Clifford代数理论方法,获得了泛欧氏空间中Clifford群、扭群、旋群及其李代数的结构及它们之间的关系,并且得到了它们的李代数. 相似文献
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《代数通讯》2013,41(4):1011-1022
ABSTRACT The algebras M a, b (E) ? E and M a+b (E) are PI equivalent over a field of characteristic 0 where E is the infinite-dimensional Grassmann algebra. This result is a part of the well-known tensor product theorem. It was first proved by Kemer in 1984–1987 (see Kemer 1991); other proofs of it were given by Regev (1990), and in several particular cases, by Di Vincenzo (1992), and by the authors (2004). Using graded polynomial identities, we obtain a new elementary proof of this fact and show that it fails for the T-ideals of the algebras M 1, 1(E) ? E and M 2(E) when the base field is infinite and of characteristic p > 2. The algebra M a, a (E) ? E satisfies certain graded identities that are not satisfied by M 2a (E). In another paper we proved that the algebras M 1, 1(E) and E ? E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities. 相似文献
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《代数通讯》2013,41(2):1033-1038
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