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1.
We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f:K→X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X2 and X×[0,1] are Q-manifolds as well. We construct a countable familyχof spaces with DDP and cd-AP such that no space X∈χis homeomorphic to the Hilbert cube Q whereas the product X×Y of any different spaces X, Y∈χis homeomorphic to Q. We also show that no uncountable familyχwith such properties exists.  相似文献   

2.
The notions of metric sparsification property and finite decomposition com- plexity are recently introduced in metric geometry to study the coarse Novikov conjecture and the stable Borel conjecture. In this paper, it is proved that a metric space X has finite decomposition complexity with respect to metric sparsification property if and only if X itself has metric sparsification property. As a consequence, the authors obtain an alterna- tive proof of a very recent result by Guentner, Tessera and Yu that all countable linear groups have the metric sparsification property and hence the operator norm localization property.  相似文献   

3.
Let A be a(left and right) Noetherian ring that is semiperfect. Let e be an idempotent of A and consider the ring Γ :=(1-e)A(1-e) and the semi-simple right A-module Se := e A/e rad A. In this paper, we investigate the relationship between the global dimensions of A and Γ, by using the homological properties of Se. More precisely, we consider the Yoneda ring Y(e) := Ext_A~*(Se, Se) of e. We prove that if Y(e) is Artinian of finite global dimension, then A has finite global dimension if and only if so does Γ. We also investigate the situation where both A and Γ have finite global dimension. When A is Koszul and finite dimensional, this implies that Y(e) has finite global dimension. We end the paper with a reduction technique to compute the Cartan determinant of Artin algebras. We prove that if Y(e) has finite global dimension, then the Cartan determinants of A and Γ coincide. This provides a new way to approach the long-standing Cartan determinant conjecture.  相似文献   

4.
We study the structure of a metric n-Lie algebra G over the complex field C. Let G = SR be the Levi decomposition, where R is the radical of G and S is a strong semisimple subalgebra of G. Denote by m(G) the number of all minimal ideals of an indecomposable metric n-Lie algebra and R ⊥ the orthogonal complement of R. We obtain the following results. As S-modules, R ⊥ is isomorphic to the dual module of G/R. The dimension of the vector space spanned by all nondegenerate invariant symmetric bilinear forms on G is equal to that of the vector space of certain linear transformations on G; this dimension is greater than or equal to m(G) + 1. The centralizer of R in G is equal to the sum of all minimal ideals; it is the direct sum of R ⊥ and the center of G. Finally, G has no strong semisimple ideals if and only if R⊥■R.  相似文献   

5.
Let τ be a premeasure on a complete separable metric space and let τ* be the Method I measure constructed from τ. We give conditions on T such that τ* has a regularity as follows: Every τ*-measurable set has measure equivalent to the supremum of premeasures of its compact subsets. Then we prove that the packing measure has this regularity if and only if the corresponding packing premeasure is locally finite.  相似文献   

6.
实对称半正定矩阵LDL~T分解的存在性与唯一性及有关问题   总被引:1,自引:0,他引:1  
The present paper proves the existence and uniqueness (in some given sense) ofthe LDL~T decomposition of real symmetric non-negative definite matrices, where Lis a unit lower triangular matrix with real elements and D is a diagonal matrixwith real elements. The proof is made in a constructive way. By taking advantageof this decomposition, a criterion for the consistency of the linear equation with sucha coefficient matrix and its whole solution set (or the least-squares solution if it isinconsistent) are obtained. Since it involves no row or column permutation, the pro-cess may be combined with any sparse technique on the computer, and hence is ofpractical importance in treating the large scale sparse matrices derived from suchproblems as the structure design by finite elements methods. Finally, the stability ofsuch a decomposition is discussed and a backward error analysis is given.  相似文献   

7.
《数学学报》2020,(3):I0001-I0006
Exceptional Cycles in the Bounded Derived Categories of Quivers Peng GUO Pu ZHANG Abstract An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D^b(kQ) of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean.  相似文献   

8.
We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a fi-nite set S of invertible substitutions such that any invertible substitution can be written as Iw^oQ1^oQ2^o……^oQk,,where Iw is the inner automorphism associated with w, and ajЕS for l≤j≤k. As a consequence, M is thematrix of an invertible substitution if and only if it is a finite product of non-negative elementary matrices.  相似文献   

9.
正Exceptional Cycles in the Bounded Derived Categories of Quivers Peng GUO Pu ZHANG Abstract An exceptional n-cycle in a Hom-finite triangulated category with Serre functor has been recently introduced by Broomhead,Pauksztello and Ploog.When n=1,it is a spherical object.We explicitly determine all the exceptional cycles in the bounded derived category D~b(kQ) of a finite quiver Q without oriented cycles.In particular,if Q is an Euclidean  相似文献   

10.
An r-uniform graph C is dense if and only if every proper subgraph G' of G satisfies λ(G') λ(G).,where λ(G) is the Lagrangian of a hypergraph G. In 1980's, Sidorenko showed that π(F), the Turán density of an γ-uniform hypergraph F is r! multiplying the supremum of the Lagrangians of all dense F-hom-free γ-uniform hypergraphs. This connection has been applied in the estimating Turán density of hypergraphs. When γ=2 the result of Motzkin and Straus shows that a graph is dense if and only if it is a complete graph. However,when r ≥ 3, it becomes much harder to estimate the Lagrangians of γ-uniform hypergraphs and to characterize the structure of all dense γ-uniform graphs. The main goal of this note is to give some sufficient conditions for3-uniform graphs with given substructures to be dense. For example, if G is a 3-graph with vertex set [t] and m edges containing [t-1]~(3),then G is dense if and only if m≥{t-2 3)+(t-2 2)+1. We also give a sufficient condition on the number of edges for a 3-uniform hypergraph containing a large clique minus 1 or 2 edges to be dense.  相似文献   

11.
C(P)系对幺半群的刻画   总被引:1,自引:1,他引:0  
设S是幺半群.本文介绍并研究了正则右系的一个推广.一个右S-系A称为C(P)系,如果A的所有循环子系满足条件(P).本文证明了右C(P)系形成了右S-系的一个新的类,同时,C(P)性质为幺半群同调分类研究提供了新思路.  相似文献   

12.
(1)设R是左连续环,则R是左Artin环当且仅当R满足左限制有限条件当且仅当R关于本质左理想满足极小条件当且仅当R关于本质左理想满足极大条件.同时给出一个左自内射环是QF环的充要条件;(2)证明了左Z1-环上的有限生成模都有Artin-Rees性质.  相似文献   

13.
After recapitulating the rudiments of the Kurosh-Amitsur radical theory of S-acts, hereditary radicals are discussed. The hereditary Hoehnke radical assignments r which designate a Rees congruence r(A) to each S-act A, are the hereditary Kurosh-Amitsur radical assignments. Then the corresponding radical as well as semisimple classes are characterized. Equivalence classes of injective S-acts determine hereditary torsion assignments t, these are just the hereditary Hoehnke radicals, but the congruence t(A) of A need not be a Rees congruence. Torsion and torsionfree classes are characterized; several hereditary torsion assignments may determine the same torsion class which is always a radical class closed under taking subacts. Examples show that a hereditary torsion assignment need not be a hereditary radical.  相似文献   

14.
We consider monoids $S=G\dot \cup I$ where G is a group and I is an ideal of S and show that if an S-act is principally weakly flat, (weakly) flat, torsion free or satisfies conditions (P) or (PE) as an I1-act, then it has these properties as an S-act. We also show that an S-act which is free, projective or strongly flat as an I1-act may not generally have these properties as an S-act.  相似文献   

15.
本文考虑拟内射、伪内射、核内射以及支内射S-系的性质,重点讨论这些广义内射S-系的上的线性方程组的性质.例如,A是核内射S-系当且仅当A的任意收缩核B上的任意A-相容线性方程组在B上是可解的;A是支内射S-系当且仅当同构于A的任一分支的S-系B上的任意A-相容线性方程组在B上是可解的.进而讨论了伪内射、核内射以及支内射S-系的融合余积的性质.最后给出了一个充分条件,基于此条件核内射和支内射S-系是等价的.  相似文献   

16.
Craig Miller 《代数通讯》2019,47(2):782-799
The purpose of this article is to introduce the theory of presentations of monoids acts. We aim to construct “nice” general presentations for various act constructions pertaining to subacts and Rees quotients. More precisely, given an M-act A and a subact B of A, on the one hand, we construct presentations for B and the Rees quotient A/B using a presentation for A, and on the other hand, we derive a presentation for A from presentations for B and A/B. We also construct a general presentation for the union of two subacts. From our general presentations, we deduce a number of finite presentability results. Finally, we consider the case where a subact B has a finite complement in an M-act A. We show that if M is a finitely generated monoid and B is finitely presented, then A is finitely presented. We also show that if M belongs to a wide class of monoids, including all finitely presented monoids, then the converse also holds.  相似文献   

17.
18.
Letd be a derivation of an associative ringR, and letM be a leftR-module withd-derivationD of finite index. It is shown thatM satisfies any of a class of conditions (including ACC, DCC, uniform, Gabriel, Krull dimension) if and only if it satisfies the same condition with respect toD-invariant submodules. If in addition 1/w! ∈R, wherew denotes the index ofd, thenD-simpleR-modules are completely reducible. Relationships between the Jacobson and theD-invariant Jacobson radicals ofM are investigated.  相似文献   

19.
A Generalization of Regular Left Acts   总被引:1,自引:0,他引:1  
AGeneralizationofRegularLeftActs*)LiuZhongkui(刘仲奎)(DepartmentofMathematics,NorthwestNormalUniversity,Lanzhou,730070)J.Ahsan(D...  相似文献   

20.
刘仲奎 《数学学报》1995,38(6):817-823
设S是左完全幺半群.本文讨论了左,右S-系的链条件,特别地证明了右S-系的Bjork定理.  相似文献   

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