共查询到20条相似文献,搜索用时 15 毫秒
1.
J. Płonka 《Southeast Asian Bulletin of Mathematics》2002,25(3):495-502
We consider algebras of a type , without nullary fundamental operation symbols. A structural property p of an identity of type is hereditary if for every set I of identities of type having the property p every consequence of I (derived identity) has the property p. An algebra
of type we call characteristic for a hereditary property p if for every variety V of type we have:
V if and only if every identity from Id(V) has the property p. In this paper we show minimal characteristic algebras for several hereditary properties, e.g., to be regular, to be normal, etc.1991 Mathematics Subject Classification
08B05 相似文献
2.
本文利用初等刀法简捷地推广了Paule的结果,从而得到了一系列多重Rogers-Ramanujan恒等式. 相似文献
3.
《代数通讯》2013,41(7):3311-3326
Abstract Let R be a prime ring and 𝒰(R) its group of units. We prove that if 𝒰(R) satisfies a group identity and 𝒰(R) generates R,then either R is a domain or R is isomorphic to the algebra of n × n matrices over a finite field of order d. Moreover the integers n and d depend only on the group identity satisfed by 𝒰(R). This result has been recently proved by C. H. Liu and T. K. Lee (Liu,C. H.; Lee,T. K. Group identities and prime rings generated by units. Comm. Algebra (to appear)) and here we present a new different proof. 相似文献
4.
5.
Xiao Mei Yang 《数学学报(英文版)》2010,26(6):1115-1124
In this paper we establish two theta function identities with four parameters by the theory of theta functions. Using these identities we introduce common generalizations of Hirschhorn-Garvan-Borwein cubic theta functions, and also re-derive the quintuple product identity, one of Ramanujan's identities, Winquist's identity and many other interesting identities. 相似文献
6.
L. M. Samoilov 《Mathematical Notes》1999,65(2):208-213
In the paper, trinomial identities of associative algebras over an infinite field are considered (in general, the algebras
may have no unit), i.e., identities of the formα
m
1+β
m
2+γ
m
3=0, where α, β, and γ are scalars andm
1,m
2, andm
3 are different monomials. It is shown that any nontrivial identity if this kind implies a semigroup identity. The algebras
with trinomial identities are characterized in the language of varieties.
Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 254–260, February, 1999. 相似文献
7.
《代数通讯》2013,41(10):5003-5010
Abstract Let R be a prime ring of characteristic different from 2, d a non-zero derivation of R, I a non-zero right ideal of R, a ∈ R, S 4(x 1,…, x 4) the standard polynomial in 4 variables. Suppose that, for any x, y ∈ I, a[d([x, y]), [x, y]] = 0. If S 4(I, I, I, I)I ≠ 0, then aI = ad(I) = 0. 相似文献
8.
Ira M. Gessel 《Journal of Combinatorial Theory, Series A》2008,115(8):1417-1435
We introduce an elementary method to give unified proofs of the Dyson, Morris, and Aomoto identities for constant terms of Laurent polynomials. These identities can be expressed as equalities of polynomials and thus can be proved by verifying them for sufficiently many values, usually at negative integers where they vanish. Our method also proves some special cases of the Forrester conjecture. 相似文献
9.
Victor J.W. Guo 《Discrete Mathematics》2008,308(9):1756-1759
We first give a bijective proof of Gould's identity in the model of binary words. Then we deduce Rothe's identity from Gould's identity again by a bijection, which also leads to a double-sum extension of the q-Chu-Vandermonde formula. 相似文献
10.
Chang Lin Mai-mai Lin 《Communications in Nonlinear Science & Numerical Simulation》2010,15(2):232-237
A type of higher dimensional loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarchy of equations, is obtained by taking use of the zero curvature equation, whose Hamiltonian structure is worked out by employing the constructed quadratic identity. 相似文献
11.
William Y.C. Chen Qing-Hu Hou Lisa H. Sun 《Journal of Combinatorial Theory, Series A》2011,118(3):899-907
We present a method for proving q-series identities by combinatorial telescoping, in the sense that one can transform a bijection or a classification of combinatorial objects into a telescoping relation. We shall illustrate this method by giving a combinatorial derivation of Watson's identity, which implies the Rogers-Ramanujan identities. 相似文献
12.
13.
Let R be a prime ring of characteristic different from 2 with Z the center of R and d a nonzero derivation of R. Let k, m, n be fixed positive integers. If ([d(x k ), x k ] n ) m ∈ Z for all x ∈ R, then R satisfies S 4, the standard identity in 4 variables. 相似文献
14.
Nihan Baydar Yarbil 《代数通讯》2018,46(1):205-216
15.
We introduce the notion of the cutting strip of an outside decomposition of a skew shape, and show that cutting strips are in one-to-one correspondence with outside decompositions for a given skew shape. Outside decompositions are introduced by Hamel and Goulden and are used to give an identity for the skew Schur function that unifies the determinantal expressions for the skew Schur functions including the Jacobi-Trudi determinant, its dual, the Giambelli determinant and the rim ribbon determinant due to Lascoux and Pragacz. Using cutting strips, one obtains a formula for the number of outside decompositions of a given skew shape. Moreover, one can define the basic transformations which we call the twist transformation among cutting strips, and derive a transformation theorem for the determinantal formula of Hamel and Goulden. The special case of the transformation theorem for the Giambelli identity and the rim ribbon identity was obtained by Lascoux and Pragacz. Our transformation theorem also applies to the supersymmetric skew Schur function. 相似文献
16.
It is proved that the exponential growth rate of identities in any superalgebra with a nilpotent commutator subalgebra over
a field of zero characteristic is an integer.
Supported by RFBR (project Nos. 07-01-00080 and 06-01-00485) and by the Council for Grants (under RF President) and State
Aid of Leading Scientific Schools (grant NSh-1983.2008.1).
Translated from Algebra i Logika, Vol. 47, No. 5, pp. 617–645, September–October, 2008. 相似文献
17.
Applications of residues to combinatorial identities 总被引:1,自引:0,他引:1
I-Chiau Huang 《Proceedings of the American Mathematical Society》1997,125(4):1011-1017
A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon's master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.
18.
We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson's rank. These symmetries are established by direct bijections. 相似文献
19.
Qinglun Yan 《Discrete Mathematics》2009,309(8):2589-2591
By means of Liouville’s theorem and the log-derivative method, we give a new proof of the septuple product identity. 相似文献
20.
Chang Xing MIAO You Bin ZHU 《数学学报(英文版)》2008,24(1):17-26
The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure{utt-△u=-F1(|u|^2,|v|^2)u,utt-△u=-F2(|u|^2,|v|^2)u where there exists a function F(λ,μ) such that δF(λ,μ)/δλ=F1(λ,μ).δF(λ,μ)/δμ=F2(λ,μ) By showing that the energy and dilation identities hold for weak solution under some assumptions on the non-linearities, we prove the global well-posedness in energy space by a similar argument to that for global regularity as shown in "Shatah and Struwe's paper, Ann. of Math. 138, 503-518 (1993)". 相似文献