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1.
Let c(x 1,?…?,?x d ) be a multihomogeneous central polynomial for the n?×?n matrix algebra M n (K) over an infinite field K of positive characteristic p. We show that there exists a multihomogeneous polynomial c 0(x 1,?…?,?x d ) of the same degree and with coefficients in the prime field 𝔽 p which is central for the algebra M n (F) for any (possibly finite) field F of characteristic p. The proof is elementary and uses standard combinatorial techniques only. 相似文献
2.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
3.
Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t;σ]∕fK[t;σ] obtained when the twisted polynomial f∈K[t;σ] is invariant, and were first defined by Petit. We compute all their automorphisms if σ commutes with all automorphisms in AutF(K) and n≥m?1, where n is the order of σ and m the degree of f, and obtain partial results for n<m?1. In the case where K∕F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic. 相似文献
4.
Diego Dominici 《The Ramanujan Journal》2008,15(3):303-338
We analyze the Krawtchouk polynomials K
n
(x,N,p,q) asymptotically. We use singular perturbation methods to analyze them for N→∞, with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain
[0,N]×[0,N], involving some special functions. We give numerical examples showing the accuracy of our formulas.
相似文献
5.
Andrs Kro 《Journal of Approximation Theory》2002,118(2):235-245
Let K
d be a compact set with a smooth boundary and consider a polynomial p of total degree n such that pC(K)1. Then we show that DTp(x)=o(n2) for any x Bd K and T a tangential direction at x. Moreover, the o(n2) term is given in terms of the modulus of smoothness of Bd K. 相似文献
6.
Kaplansky asked about the possible images of a polynomial f in several noncommuting variables. In this paper, we consider the case of f a Lie polynomial. We describe all the possible images of f in M2(K) and provide an example of f whose image is the set of non-nilpotent trace zero matrices, together with 0. We provide an arithmetic criterion for this case. We also show that the standard polynomial sk is not a Lie polynomial, for k>2. 相似文献
7.
We develop the general theory for a new functor K
e on the category of C
*-algebras. The extremal K-set, K
e
(A), of a C
*-algebra A is defined by means of homotopy classes of extreme partial isometries. It contains K
1
(A) and admits a partially defined addition extending the addition in K
1
(A), so that we have an action of K
1
(A) on K
e
(A). We show how this functor relates to K
0 and K
1, and how it can be used as a carrier of information relating the various K-groups of ideals and quotients of A. The extremal K-set is then used to extend the classical theory of index for Fredholm and semi-Fredholm operators. 相似文献
8.
With the notation
,we prove the following result.Theorem 1. Assume that p is a trigonometric polynomial of degree at most n with real coefficients that satisfiesThenwithWe also prove thatandfor every
, where
denotes the collection of all trigonometric polynomials of the form 相似文献
||p||L2(K)An1/2 and ||p′||L2(K)Bn3/2.
M4(p)−M2(p)M2(p)
M2(p)−M1(p)10−31M2(p)
9.
Let Top
0
be the category of topological T
0-spaces, QU
0
the category of quasi-uniform T
0-spaces, T : QU
0
→ Top
0
the usual forgetful functor and K : QU
0
→ QU
0
the bicompletion reflector with unit k : 1 → K. Any T-section F : Top
0
→ QU
0
is called K-true if KF = FTKF, and upper (lower)
K-true if KF is finer (coarser) than FTKF. The literature considers important T-sections F that enjoy all three, or just one, or none of these properties. It is known that T(K,k)F is well-pointed if and only if F is upper K-true. We prove the surprising fact that T(K,k)F is the reflection to Fix(TkF) whenever it is idempotent. We also prove a new characterization of upper K-trueness. We construct examples to set apart some natural cases. In particular we present an upper K-true F for which T(K,k)F is not idempotent, and a K-true F for which the coarsest associated T-preserving coreflector in QU
0
is not stable under K.
We dedicate this paper to the memory of Sérgio de Ornelas Salbany (1941–2005). 相似文献
10.
Let g(x) be a monic irreducible defectless polynomial over a henselian valued field (K, v), i.e., K(θ) is a defectless extension of (K, v) for any root θ of g(x). It is known that a complete distinguished chain for θ with respect to (K, v) gives rise to several invariants associated with g(x). Recently Ron Brown studied certain invariants of defectless polynomials by introducing strict systems of polynomial extensions. In this article, the authors establish a one-to-one correspondence between strict systems of polynomial extensions and conjugacy classes of complete distinguished chains. This correspondence leads to a simple interpretation of various results proved for strict systems. The authors give new characterizations of an invariant γ g introduced by Brown. 相似文献
11.
Jerzy BROWKIN 《数学年刊B辑(英文版)》2007,28(5):507-520
In "Elements of small orders in K2(F)" (Algebraic K-Theory, Lecture Notes in Math., 966, 1982, 1-6.), the author investigates elements of the form {a, Φn(a)} in the Milnor group K2F of a field F, where Φn(x) is the n-th cyclotomic polynomial. In this paper, these elements are generalized. Applying the explicit formulas of Rosset and Tate for the transfer homomorphism for K2, the author proves some new results on elements of small orders in K2F. 相似文献
12.
Meng-xiao Yin 《应用数学学报(英文版)》2006,22(3):451-456
Let a(Kr,+1 - K3,n) be the smallest even integer such that each n-term graphic sequence п= (d1,d2,…dn) with term sum σ(п) = d1 + d2 +…+ dn 〉 σ(Kr+1 -K3,n) has a realization containing Kr+1 - K3 as a subgraph, where Kr+1 -K3 is a graph obtained from a complete graph Kr+1 by deleting three edges which form a triangle. In this paper, we determine the value σ(Kr+1 - K3,n) for r ≥ 3 and n ≥ 3r+ 5. 相似文献
13.
The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25). 相似文献
14.
For given a graph H, a graphic sequence π = (d
1, d
2,..., d
n) is said to be potentially H-graphic if there is a realization of π containing H as a subgraph. In this paper, we characterize the potentially (K
5 − e)-positive graphic sequences and give two simple necessary and sufficient conditions for a positive graphic sequence π to
be potentially K
5-graphic, where K
r is a complete graph on r vertices and K
r-e is a graph obtained from K
r by deleting one edge. Moreover, we also give a simple necessary and sufficient condition for a positive graphic sequence
π to be potentially K
6-graphic.
Project supported by National Natural Science Foundation of China (No. 10401010). 相似文献
15.
Antônio Pereira BrandãoJr Plamen Koshlukov Alexei Krasilnikov 《Monatshefte für Mathematik》2009,157(3):247-256
Let K be an infinite integral domain, and let A = M
2(K) be the matrix algebra of order two over K. The algebra A can be given a natural -grading by assuming that the diagonal matrices are the 0-component while the off-diagonal ones form the 1-component. In
this paper we study the graded identities and the graded central polynomials of A. We exhibit finite bases for these graded identities and central polynomials. It turns out that the behavior of the graded
identities and central polynomials in the case under consideration is much like that in the case when K is an infinite field of characteristic 0 or p > 2. Our proofs are characteristic-free so they work when K is an infinite field, char K = 2. Thus we describe finite bases of the graded identities and graded central polynomials for M
2(K) in this case as well.
A. Krasilnikov has been partially supported by CNPq and FINATEC. 相似文献
16.
Abstract In 1956, Ehrenfeucht proved that a polynomial f 1(x 1) + · + f n (x n ) with complex coefficients in the variables x 1, …, x n is irreducible over the field of complex numbers provided the degrees of the polynomials f 1(x 1), …, f n (x n ) have greatest common divisor one. In 1964, Tverberg extended this result by showing that when n ≥ 3, then f 1(x 1) + · + f n (x n ) belonging to K[x 1, …, x n ] is irreducible over any field K of characteristic zero provided the degree of each f i is positive. Clearly a polynomial F = f 1(x 1) + · + f n (x n ) is reducible over a field K of characteristic p ≠ 0 if F can be written as F = (g 1(x 1)) p + (g 2(x 2)) p + · + (g n (x n )) p + c[g 1(x 1) + g 2(x 2) + · + g n (x n )] where c is in K and each g i (x i ) is in K[x i ]. In 1966, Tverberg proved that the converse of the above simple fact holds in the particular case when n = 3 and K is an algebraically closed field of characteristic p > 0. In this article, we prove an extension of Tverberg's result by showing that this converse holds for any n ≥ 3. 相似文献
17.
Let K
m,nbe a complete bipartite graph with two partite sets having m and n vertices, respectively. A K
p,q-factorization of K
m,n is a set of edge-disjoint K
p,q-factors of K
m,n which partition the set of edges of K
m,n. When p = 1 and q is a prime number, Wang, in his paper “On K
1,k
-factorizations of a complete bipartite graph” (Discrete Math, 1994, 126: 359—364), investigated the K
1,q
-factorization of K
m,nand gave a sufficient condition for such a factorization to exist. In the paper “K
1,k
-factorizations of complete bipartite graphs” (Discrete Math, 2002, 259: 301—306), Du and Wang extended Wang’s result to the
case that q is any positive integer. In this paper, we give a sufficient condition for K
m,n to have a K
p,q-factorization. As a special case, it is shown that the Martin’s BAC conjecture is true when p : q = k : (k+ 1) for any positive integer k. 相似文献
18.
Algebraic K-Theory and the Conjectural Leibniz K-Theory 总被引:1,自引:0,他引:1
Jean-Louis Loday 《K-Theory》2003,30(2):105-127
The analogy between algebraic K-theory and cyclic homology is used to build a program aiming at understanding the algebraic K-theory of fields and the periodicity phenomena in algebraic K-theory. In particular, we conjecture the existence of a Leibniz K-theory which would play the role of Hochschild homology. We propose a motivated presentation for the Leibniz K
2-group ofa field. 相似文献
19.
Tong Liu 《中国科学A辑(英文版)》1999,42(10):1009-1018
LetK
6 be a real cyclic sextic number field, andK
2,K
3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh
- =h (K
6)/(h(K
2)h(K
3)) are obtained. In particular, when the conductorf
6 ofK
6 is a primep,
, whereC is an explicitly given constant, andB
n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic
quartic fields.
Project supported by the National Natural Science Foundation of China (Grant No. 19771052). 相似文献
20.
Let K
m
-H be the graph obtained from K
m
by removing the edges set E(H) of H where H is a subgraph of K
m
. In this paper, we characterize the potentially K
5-P
4 and K
5-Y
4-graphic sequences where Y
4 is a tree on 5 vertices and 3 leaves.
Research was supported by NNSF of China (10271105) and by NSF of Fujian (Z0511034), Fujian Provincial Training Foundation
for “Bai-Quan-Wan Talents Engineering”, Project of Fujian Education Department, Project of Zhangzhou Teachers College and
by NSERC. 相似文献