共查询到20条相似文献,搜索用时 234 毫秒
1.
设Q是有限置换右R模,则EndR(Q)是可分环当且仅当对所有A,B∈FP(Q),A A≌A B≌B B A≤ B或B≤ A.作为应用得到了EndR(P Q)是可分环当且仅当EndRP和EndRQ为可分环,其中P,Q为有限置换右R模. 相似文献
2.
给出了环R上幂等矩阵P,Q满足不同条件:(1)PQP=0;(2)PQP=PQ;(3)PQ=QP;(4)PQP=P时P+aQ的Drazin逆的表达式,推广了一些已有的结论. 相似文献
3.
4.
陈焕艮 《数学年刊A辑(中文版)》2003,(4)
设Q是有限置换右R模,则End_R(Q)是可分环当且仅当对所有A,B∈FP(Q),A AA B B B A≤ B或 B≤A,作为应用得到了 End_R(P Q)是可分环当且仅当End_R P和End_R Q为可分环,其中P,Q为有限置换右R模。 相似文献
5.
6.
W·Burgess 和 M·Chacron 在文献〔1〕中刻划了亚直不可约 DQC 环·所谓 DQC 环R,就是 R 的任何理想 I 均由 I∩Q 生成的,这里 Q 称为 R 的拟中心,即 Q={r∈R|对任何 s∈R,存在 s′、s″∈R 使得 rs=s′r 和 sr=rs″}.显然,交换环、有1之双环(单边理想均为双边理想之环)都是 DQC 环.本文给出了 DQC 环具理想升链条件的一个充分必要条件以及 krull 交定理在 DQC 环中的一个推广.如无特别说明,本文中的理想均指双边理想,R 表示 DQC 环,Q 表示 R 的拟中心,(a)表示由元素a∈R 生成的双边理想.根据拟中心 Q 的定义,我们有:对任何a∈Q,(a)={ar+ma|r∈R,m 是整数}={ra 相似文献
7.
In this paper, we consider the following nonlinear coupled elliptic systems with continuous potentials:{-ε~2?u +(1 + δP(x))u = μ1 u~3+ βuv~2 in ?,-ε~2?v +(1 + δQ(x))v = μ2 v~3+ βu~2 v in ?,u 0, v 0 in ?,(?u)/(?v)=(?ν)/(?ν)=0on ??,(A_ε)where ? is a smooth bounded domain in R~N for N = 2, 3, δ, ε, μ_1 and μ_2 are positive parameters, β∈ R,P(x) and Q(x) are two smooth potentials defined on ?, the closure of ?. Due to Liapunov-Schmidt reduction method, we prove that(A_ε) has at least O(1/(ε| ln ε|)~N) synchronized and O(1/(ε| ln ε|)~(2 N)) segregated vector solutions for ε and δ small enough and some β∈ R. Moreover, for each m ∈(0, N) there exist synchronized and segregated vector solutions for(A_ε) with energies in the order of ε~(N-m). Our results extend the result of Lin et al.(2007) from the Lin-Ni-Takagi problem to the nonlinear Schr¨odinger elliptic systems with continuous potentials. 相似文献
8.
9.
10.
设A是域k上的有限维代数,(Q,I)是带关系的箭图,令Λ=AkkQ/I.Λ的模范畴Λ-Mod及有限生成模范畴Λ-mod分别与(Q,I)在A上的表示范畴Rep(Q,I,A)及有限维表示范畴rep(Q,I,A)等价.给出了范畴rep(A_3,I,A)中Gorenstein投射模的具体构造,其中(A_3,I)=3α→2β→1,I=<βα>.在此基础上,给出了代数A是自入射代数的一个充分必要条件. 相似文献
11.
Let B(H) be the algebra of all the bounded linear operators on a Hilbert space H.For A,P and Q in B(H),if there exists an operator X∈ B(H) such thatAP X QA=A,X QAP X=X,(QAP X)*=QAP X and(X QAP)*=X QAP,then X is said to be the Γ-inverse of A associated with P and Q,and denoted by AP,Q+.In this note,we present some necessary and su?cient conditions for which A+P,Qexists,and give an explicit representation of AP,Q+(if AP,Q+exists). 相似文献
12.
13.
Viorel Barbu 《Journal of Mathematical Analysis and Applications》1981,80(2):566-597
In 1956, R. Penrose studied best-approximate solutions of the matrix equation AX = B. He proved that A+B (where A+ is the Moore-Penrose inverse) is the unique matrix of minimal Frobenius norm among all matrices which minimize the Frobenius norm of AX ? B. In particular, A+ is the unique best-approximate solution of AX = I. The vector version of Penrose's result (that is, the fact that the vector A+b is the best-approximate solution in the Euclidean norm of the vector equation Ax = b) has long been generalized to infinite dimensional Hilbert spaces.In this paper, an infinite dimensional version of Penrose's full result is given. We show that a straightforward generalization is not possible and provide new extremal characterizations (in terms of the Hermitian order) of A+ and of the classes of generalized inverses associated with minimal norm solutions of consistent operator equations or with least-squares solutions. For a certain class of operators, we can phrase our characterizations in terms of a whole class of norms (including the Hilbert-Schmidt and the trace norms), thus providing new extremal characterizations even in the matrix case. We treat both operators with closed range and with not necessarily closed range. Finally, we characterize A+ as the unique inner inverse of minimal Hilbert-Schmidt norm if ∥A+∥2 < ∞. We give an application of the new extremal characterization to the compensation problem in systems analysis in infinite-dimensional Hilbert spaces. 相似文献
14.
We consider Lyapunov's equationPA+A
T
P+Q=0, whereQ is symmetric positive definite andA is in controllable companion form. We prove that a necessary and sufficient condition thatA be stable is that the first rowP
1 of theP-matrix be a stablen–1 coefficient vector. This result is related to the minimum phase property of linear systems and is useful in designing robust controllers. 相似文献
15.
Let A be a commutative ring and I an ideal of A with a reduction Q. In this article, we give an upper bound on the reduction number of I with respect to Q, when a suitable family of ideals in A is given. As a corollary it follows that if some ideal J containing I satisfies J 2 = QJ, then I v+2 = QI v+1, where v denotes the number of generators of J/I as an A-module. 相似文献
16.
In this paper we generalize the plus-construction given by M. Livernet for algebras over rational differential graded operads to the framework of cofibrant operads over an arbitrary ring (the category of algebras over such operads admits a closed model category structure). We follow the modern approach of J. Berrick and C. Casacuberta defining topological plus-construction as a nullification with respect to a universal acyclic space. We construct a universalH
*Q-acyclic algebra and we define A A+ as the -nullification of the algebra A. This map induces an isomorphism in Quillen homology and quotients out the maximal perfect ideal of 0(A). As an application, we consider for any associative algebra R the plus-constructions of gl(R) in the categories of homotopy Lie and homotopy Leibniz algebras. This gives rise to two new homology theories for associative algebras, namely homotopy cyclic and homotopy Hochschild homologies. Over the rationals these theories coincide with the classical cyclic and Hochschild homologies.Primary: 19D06, 19D55; Secondary: 18D50, 18G55, 55P60, 55U35Received March 2003 相似文献
17.
In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (ΔE,ΔA) such that (E+ΔE,A+ΔA) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set by introducing dissipative Hamiltonian matrix pairs: A matrix pair (E,A) is dissipative Hamiltonian if A=(J−R)Q with skew‐symmetric J, positive semidefinite R, and an invertible Q such that QTE is positive semidefinite. This reformulation has a convex feasible domain onto which it is easy to project. This allows us to employ a fast gradient method to obtain a nearby stable approximation of a given matrix pair. 相似文献
18.
19.
Jürgen Herzog 《manuscripta mathematica》1977,21(4):307-314
Let RA be a local inclusion of noetherian local rings. Assume that R is an algebra retract of A with the local retraction mapping p:AR. Let M be an R-module of finite type. Considering M as A-module via p we get P
M
A
=P
R
A
P
M
R
(Th. 1), where P
N
S
denotes the Poincaréseries of an S-module N. This result is used to give a simple proof of Th. 1 in [2], Also an application to fibre products of rings is given (Th. 2), generalizing slightly a result due to A. Dress and H. Krämer, see [1]. 相似文献
20.
《Quaestiones Mathematicae》2013,36(1-3):155-166
Abstract Let A be a von Neumann algebra on a Hilbert space H and let P(A) denote the projections of A. A comparative probability (CP) on A (or more correctly on P(A)) is a preorder ? on P(A) satisfying: 0 ? P ? P ε P(A) with Q ≠ 0 for some Q ε P(A). If P, Q ε P(A) then either P ? Q or Q ? P. If P, Q and R are all in P(A) and P⊥R, Q⊥R, then P ? Q ? P + R ? Q + R. Let τ be any of the usual locally convex topologies on A. We say ? is τ continuous if the interval topology induced on P(A) by ? is weaker than the τ topology on P(A). If μ an additive (completely additive) measure on P(A) then μ induces a uniformly (weakly) continuous CP ?μ on P(A) given by P ?μ Q if μ(P) ? μ(Q). We show that if A is the C* algebra C(H) of compact operators on an infinite dimensional Hilbert space H, the converse is true under an extra boundedness condition on the CP which is automatically satisfied whenever the identity is present in A = P(C(H)). 相似文献