共查询到20条相似文献,搜索用时 15 毫秒
1.
《代数通讯》2013,41(2):869-875
Abstract Given a contravariant functor F : 𝒞 → 𝒮ets for some category 𝒞, we say that F (𝒞) (or F) is generated by a pair (X, x) where X is an object of 𝒞 and x ∈ F(X) if for any object Y of 𝒞 and any y ∈ F(Y), there is a morphism f : Y → X such that F(f)(x) = y. Furthermore, when Y = X and y = x, any f : X → X such that F(f)(x) = x is an automorphism of X, we say that F is minimally generated by (X, x). This paper shows that if the ring R is left noetherian, then there exists a minimal generator for the functor ?xt (?, M) : ? → 𝒮ets, where M is a left R-module and ? is the class (considered as full subcategory of left R-modules) of injective left R-modules. 相似文献
2.
A family of permutations ℱ ⊆ Sn with a probability distribution on it is called k-restricted min-wise independent if we have Pr[min π(X) = π(x)] = 1/|X| for every subset X ⊆ [n] with |X| ≤ k, every x ∈ X, and π ∈ ℱ chosen at random. We present a simple proof of a result of Norin: every such family has size at least Some features of our method might be of independent interest. The best available upper bound for the size of such family is 1 + ∑ (j − 1)(). We show that this bound is tight if the goal is to imitate not the uniform distribution on Sn, but a distribution given by assigning suitable priorities to the elements of [n] (the stationary distribution of the Tsetlin library, or self-organizing lists). This is analogous to a result of Karloff and Mansour for k-wise independent random variables. We also investigate the cases where the min-wise independence condition is required only for sets X of size exactly k (where we have only an Ω(log log n + k) lower bound), or for sets of size k and k − 1 (where we already obtain a lower bound of n − k + 2). © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003 相似文献
3.
《代数通讯》2013,41(1):379-389
Abstract Let d 1 : k[X] → k[X] and d 2 : k[Y] → k[Y] be k-derivations, where k[X] ? k[x 1,…,x n ], k[Y] ? k[y 1,…,y m ] are polynomial algebras over a field k of characteristic zero. Denote by d 1 ⊕ d 2 the unique k-derivation of k[X, Y] such that d| k[X] = d 1 and d| k[Y] = d 2. We prove that if d 1 and d 2 are positively homogeneous and if d 1 has no nontrivial Darboux polynomials, then every Darboux polynomial of d 1 ⊕ d 2 belongs to k[Y] and is a Darboux polynomial of d 2. We prove a similar fact for the algebra of constants of d 1 ⊕ d 2 and present several applications of our results. 相似文献
4.
Karen E. Smith 《代数通讯》2013,41(12):5915-5929
Abstract For a canonical threefold X, we know that h 0(X, 𝒪 X (nK X )) ≥ 1 for a sufficiently large n. When χ(𝒪 X ) > 0, it is not easy to get such an integer n. Fletcher showed that h 0(X, 𝒪 X (12K X )) ≥ 1 and h 0(X, 𝒪 X (24K X )) ≥ 2 when χ(𝒪 X ) = 1. He inquired about existence of a canonical threefold with given conditions which shows the result sharp. We show that such an example does not exist. Using a different technique, we prove h 0(X, 𝒪 X (12K X )) ≥ 2. 相似文献
5.
W.-M. Wang 《偏微分方程通讯》2013,38(12):2164-2179
We consider the Aharonov–Bohm effect for the Schrödinger operator H = (?i? x ? A(x))2 + V(x) and the related inverse problem in an exterior domain Ω in R 2 with Dirichlet boundary condition. We study the structure and asymptotics of generalized eigenfunctions and show that the scattering operator determines the domain Ω and H up to gauge equivalence under the equal flux condition. We also show that the flux is determined by the scattering operator if the obstacle Ω c is convex. 相似文献
6.
Zoltn Füredi 《Random Structures and Algorithms》1996,8(2):97-104
The following result is proved by using entropy of hypergraphs. If π1, …, πd are permutations of the n element set P such that for every triple x, y, z ϵ P, one can find a πi such that πi(x) is between πi(y) and πi(z), then n <exp(d/2). We also study k-scrambling permutations. Several problems remained open. © 1996 John Wiley & Sons, Inc. 相似文献
7.
Lingling Fan 《代数通讯》2013,41(6):2021-2029
Let R be an associative ring with identity. An element a ∈ R is called clean if a = e + u with e an idempotent and u a unit of R, and a is called strongly clean if, in addition, eu = ue. A ring R is clean if every element of R is clean, and R is strongly clean if every element of R is strongly clean. When is a matrix ring over a strongly clean ring strongly clean? Does a strongly clean ring have stable range one? For these open questions, we prove that 𝕄 n (C(X)) is strongly π-regular (hence, strongly clean) where C(X) is the ring of all real valued continuous functions on X with X a P-space; C(X) is clean iff it has stable range one; and a unital C*-algebra in which every unit element is self-adjoint is clean iff it has stable range one. The criteria for the ring of complex valued continuous functions C(X,?) to be strongly clean is given. 相似文献
8.
Supercharacter theories for an arbitrary finite group were developed by Diaconis and Isaacs. Let G* denote the set of all π-regular elements of G. Set Iπ(G) = {χ* | χ ∈Irr(G) and χ* ≠ α* + β* for characters α, β of G}, where χ* means the restriction of χ to G*. In this paper, we consider the partitions of Iπ(G) and G* for a π-separable group G. We obtain some results which generalize those of Diaconis and Isaacs. 相似文献
9.
Jaka Cimprič 《代数通讯》2013,41(11):4035-4041
10.
Juan C. Gutiérrez Fernández 《代数通讯》2013,41(10):3760-3776
We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic ≠ 2 is solvable. We prove that every commutative finite-dimensional algebra 𝔄 over a field F of characteristic ≠ 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras. 相似文献
11.
Matej Brešar 《代数通讯》2013,41(1):154-163
Let 𝒜 be a ring, let ? be an 𝒜-bimodule, and let 𝒞 be the center of ?. A map F:𝒜 → ? is said to be range-inclusive if [F(x), 𝒜] ? [x, ?] for every x ∈ 𝒜. We show that if 𝒜 contains idempotents satisfying certain technical conditions (which we call wide idempotents), then every range-inclusive additive map F:𝒜 → ? is of the form F(x) = λx + μ(x) for some λ ∈ 𝒞 and μ:𝒜 → 𝒞. As a corollary we show that if 𝒜 is a prime ring containing an idempotent different from 0 and 1, then every range-inclusive additive map from 𝒜 into itself is commuting (i.e., [F(x), x] = 0 for every x ∈ 𝒜). 相似文献
12.
I. Alrasasi 《代数通讯》2013,41(4):1385-1400
Let D be an integral domain with quotient field K. A Bhargava ring over D is defined to be 𝔹 x (D): = {f ∈ K[X] | ? a ∈ D, f(xX + a) ∈ D[X]}, where x ∈ D. A Bhargava ring over D is a subring of the ring of integer-valued polynomials over D. In this article, we study the prime ideal structure and calculate the Krull and valuative dimension of Bhargava rings over a general domain D. 相似文献
13.
《Mathematical Methods in the Applied Sciences》2018,41(12):4560-4588
The paper deals with the reconstruction of the convolution kernel, together with the solution, in a mixed linear evolution system of hyperbolic type. This problem describes uniaxial deformations u of a cylindrical domain (0,π) × Ω, which is filled with a linear viscoelastic solid whose material properties are supposed to be uniform on Ω‐sections perpendicular to the x axis. Various types of boundary conditions in [0,T] × {0,π} × Ω are prescribed, whereas Dirichlet conditions are assumed in [0,T] × (0,π) × ∂Ω. To reconstruct both u and k, we suppose of knowing for any time tand any x ∈ (0,π) the flux of the viscoelastic stress vector through the boundary of the Ω‐section. The main novelty is that the unknown kernel k is allowed to depend, not only on the time variable t but also on the space variable x. 相似文献
14.
Let G be a finite group and τ(G) denote the number of conjugacy classes of all non-abelian subgroups of G. The symbol π(G) denotes the set of the prime divisors of |G|. In this paper, finite groups with τ(G) ≤ |π(G)| are classified completely. Furthermore, finite nonsolvable groups with τ(G) = |π(G)| +1 are determined. 相似文献
15.
Xianglin Du 《代数通讯》2013,41(4):1345-1359
ABSTRACT Let k(G) be the number of conjugacy classes of finite groups G and π e (G) be the set of the orders of elements in G. Then there exists a non-negative integer k such that k(G) = |π e (G)| + k. We call such groups to be co(k) groups. This article classifies all finite co(1) groups. They are isomorphic to one of the following groups: A 5, L 2(7), S 5, Z 3, Z 4, S 4, A 4, D 10, Hol(Z 5), or Z 3 ? Z 4. 相似文献
16.
For a Tychonoff space X,we use ↓USC F(X) and ↓C F(X) to denote the families of the hypographs of all semi-continuous maps and of all continuous maps from X to I = [0,1] with the subspace topologies of the hyperspace Cld F(X × I) consisting of all non-empty closed sets in X × I endowed with the Fell topology.In this paper,we shall show that there exists a homeomorphism h:↓USC F(X) → Q = [1,1] ω such that h(↓CF(X))=c0 = {(xn)∈Q| lim n→∞ x n = 0} if and only if X is a locally compact separable metrizable space and the set of isolated points is not dense in X. 相似文献
17.
18.
Igor Dolinka 《代数通讯》2013,41(12):5179-5198
Denote by 𝒯n and 𝒮n the full transformation semigroup and the symmetric group on the set {1,…, n}, and ?n = {1} ∪ (𝒯n?𝒮n). Let 𝒯(X, 𝒫) denote the monoid of all transformations of the finite set X preserving a uniform partition 𝒫 of X into m subsets of size n, where m, n ≥ 2. We enumerate the idempotents of 𝒯(X, 𝒫), and describe the submonoid S = ? E ? generated by the idempotents E = E(𝒯(X, 𝒫)). We show that S = S1 ∪ S2, where S1 is a direct product of m copies of ?n, and S2 is a wreath product of 𝒯n with 𝒯m?𝒮m. We calculate the rank and idempotent rank of S, showing that these are equal, and we also classify and enumerate all the idempotent generating sets of minimal size. In doing so, we also obtain new results about arbitrary idempotent generating sets of ?n. 相似文献
19.
ForX a set the expression Prt(X) denotes the composition monoid of all functionsf X ×X. Fork a positive integer the letterk denotes also the set of all nonnegative integers less thank. Whenk > 1 the expression rk denotes the connected injective element {<i, i + 1>i k – 1} in Prt (k). We show for every word w=w(x,y) in a two-letter alphabet that if the equation w(x, y)=rk has a solution =y) 2Prt(k) then ¯w(x,y)=rk also has a solution in2Prt(k), where ¯w is the word obtained by spelling the wordw backwards. It is a consequence of this theorem that if for every finite setX and for everyf Prt(X) the equation w(x,y)=f has a solution in2Prt(X) then for every suchX andf the equation ¯w(x, y)=f has a solution in2Prt(X).Presented by J. Mycielski. 相似文献
20.
Ken-Ichi Yoshikawa 《Mathematische Annalen》2007,337(1):61-89
Let π: X → S be a holomorphic map from a compact Kähler manifold (X,g X ) to a compact Riemann surface S. Let Σπ be the critical locus of π and let Δ = π(Σπ) be the discriminant locus. Let (ξ, h ξ) be a holomorphic Hermitian vector bundle on X. We determine the singularity of the Quillen metric on det Rπ*ξ near Δ with respect to g X | TX/S and h ξ. 相似文献