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1.
The topological interpretations of some of the algebraic properties of the semigroup Sn of singular endomorphisms of an n -dimensional vector space over K are discussed here. Since Sn is known to be an idempotent generated regular semigroup, we pay more attention to the topological properties of the set En of idempotents in Sn . The local structure of En is shown to be that of a C infinity-manifold and of a finite-dimensional vector bundle over the Grassmann manifolds. The topology of the biorder relations and sandwich sets are also discussed. 相似文献
2.
We study notions such as finite presentability and coherence, for partially ordered abelian groups and vector spaces. Typical results are the following: (i) A partially ordered abelian group G is finitely presented if and only if G is finitely generated as a group, G + is well-founded as a partially ordered set, and the set of minimal elements of G +\ {0} is finite. (ii) Torison-free, finitely presented partially ordered abelian groups can be represented as subgroups of some Zn , with a finitely generated submonoid of (Z+)n as positive cone. (iii) Every unperforated, finitely presented partially ordered abelian group is Archimedean. Further, we establish connections with interpolation. In particular, we prove that a divisible dimension group G is a directed union of simplicial subgroups if and only if every finite subset of G is contained into a finitely presented ordered subgroup. 相似文献
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We investigate properties of the endomorphism monoid of the countable random graph R . We show that End(R) is not regular and is not generated by its idempotents. The Rees order on the idempotents of End(R) has 2N0 many minimal elements. We also prove that the order type of Q is embeddable in the Rees order of End(R) . 相似文献
6.
The main aim of this paper is to obtain a dual result to the now well known Auslander-Bridger formula for G-dimension. We will show that if R is a complete Cohen-Macaulay ring with residue field k, and M is a non-injective h-divisible Ext-finite R-module of finite Gorenstein injective dimension such that for each i 3 1i \geq 1 Exti (E,M) = 0 for all indecomposable injective R-modules E 1 E(k)E \neq E(k), then the depth of the ring is equal to the sum of the Gorenstein injective dimension and Tor-depth of M. As a consequence, we get that this formula holds over a d-dimensional Gorenstein local ring for every nonzero cosyzygy of a finitely generated R-module and thus in particular each such nth cosyzygy has its Tor-depth equal to the depth of the ring whenever n 3 dn \geq d. 相似文献
7.
We give in this work some results about the existence and uniqueness with optimal regularity for solutions of a parabolic equation in nondivergence form in Lq (0,T;Lp (Omega)) where 1 < p,q < infinity in two cases. We use Lamberton's results (cf. [9]) in the first case and Dore-Venni's results (cf. [6]) in the second case. 相似文献
8.
C. Hainzl 《Annales Henri Poincare》2003,4(2):217-237
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Th. Bartsch 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2000,17(1):366-384
10.
Shavtak Alimov 《Journal of Fourier Analysis and Applications》2003,9(1):67-76
For eigenfunction expansions of piecewise smooth functionsassociated with an elliptic operator of order m in R 2 theconvergence is proved. 相似文献
11.
T. Shibata 《Annales Henri Poincare》2001,2(4):713-732
12.
Flores Julio; Hernandez Francisco L.; Tradacete Pedro 《Quarterly Journal of Mathematics》2008,59(3):321-334
It is proved that every positive operator R on a Banach latticeE dominated by a strictly singular operator T:E E satisfiesthat the R4 is strictly singular. Moreover, if E is order continuousthen the R2 is already strictly singular. 相似文献
13.
Let G/H be an irreducible globally hyperbolic semisimple symmetric space, and let S ³ G be a subsemigroup containing H not isolated in S . We show that if So p 0 then there are H -invariant minimal and maximal cones C min ³ C max in the tangent space at the origin such that H exp C min ³ S ³ HZK (a)expC max . A double coset decomposition of the group G in terms of Cartan subspaces and the group H is proved. We also discuss the case where G/H is of Cayley type. 相似文献
14.
A Relation between Hausdorff Dimension and a Condition on Time Sets for the Image by the Brownian Sheet to Possess Interior Points 总被引:2,自引:0,他引:2
We prove that if WN, d is a Brownian sheet mapping to Rd and E is a set in (0, )N of Hausdorff dimensiongreater than , then for almost every rotation about a point x and translation x such that x(E) (0, )N, the set x(E) is such that almost surely W(E) containsinterior points. The techniques are adapted from Kahane andRosen and generalize to higher dimensional time and range. 相似文献
15.
Let E2(T) denote the error term in the asymptotic formula forT0|(+it)|4dt. It is proved that there exist constants A>0,B>1 such that for TT0>0 every interval [T, BT] containspoints T1, T2 for which
and that T0|E2(t)|adt>>T1+(a/2) for any fixed a1. Theseresults complement earlier results of Motohashi and Ivi thatT0E2(t)dt<<T3/2 and that T0E22(t)dt<<T2logCT forsome C>0. Omega-results analogous to the above ones are obtainedalso for the error term in the asymptotic formula for the Laplacetransform of |(+it)|4. 相似文献
16.
The Canonical Decomposition of the Poset of a Hammock 总被引:1,自引:0,他引:1
In the Auslander-Reiten quiver of a representation-directedalgebra several hammocks occur naturally; they begin at theprojective cover of a simple module E and end in the correspondinginjective hull. It is known that hammocks are Auslander-Reitenquivers of posets, so there is a poset corresponding to eachsimple module; it describes the set of modules having E as acomposition factor. In this paper we show that this poset Sdecomposes canonically into a coideal S+ and an ideal S–which can easily be described by vectorspace-categories correspondingto a one-point extension or a one-point coextension, respectively.In addition, we describe the simple modules for which S+ andS– are not comparable, and also those for which S+ S–. We also show how to use the results in order to prove for certainposets that they do not occur as posets corresponding to simplemodules. 相似文献
17.
J. Leech studied certain coextensions E S , of a monoid S and Ch. Wells studied the relationship between Leech coextensions and those studied in a general categorical setting by J. Beck. In this paper it is completed some of the Wells results and it is given a classification of the Leech coextensions. Specifically, Wells shows that a Leech coextension is a Beck coextension if its corresponding functor is "centralizing" (a generalization of abelian-valued). Our Theorem 1.1 provides a technical condition under which Beck coextensions are actually abelian. This technical condition implies other properties as well. Corollary 1.8 provides three natural conditions under any of which the conditions of 1.1 are satisfied. Also it is provided an example of a non-abelian Beck coextension. Table 1 shows the general classification and Table 2 shows the reduced set of possibilities when the semigroup is a regular monoid. Stronger results are provided for coextensions with S an inverse monoid, and for extensions of groups by monoids. 相似文献
18.
In this paper, we give examples of elliptic curves E/K overa number field K satisfying the property that there exist P1,P2 K[t] such that the twists and are of positiverank over K(t). As a consequence of this result on twists, weshow that for those elliptic curves E/K, and for each , the rank of E over the fixed field (Kab) under is infinite, where Kab is the maximal abelian extension ofK. 相似文献
19.
Removable singularities for Hardy spaces Hp() = {f Hol(): |f|p u in for some harmonic u}, 0 < p < are studied. A setE = is a weakly removable singularity for Hp(\E) if Hp(\E) Hol(), and a strongly removable singularity for Hp(\E) if Hp(\E)= Hp(). The two types of singularities coincide for compactE, and weak removability is independent of the domain . The paper looks at differences between weak and strong removability,the domain dependence of strong removability, and when removabilityis preserved under unions. In particular, a domain and a setE that is weakly removable for all Hp, but not strongly removablefor any Hp(\E), 0 < p < , are found. It is easy to show that if E is weakly removable for Hp(\E)and q > p, then E is also weakly removable for Hq(\E). Itis shown that the corresponding implication for strong removabilityholds if and only if q/p is an integer. Finally, the theory of Hardy space capacities is extended, anda comparison is made with the similar situation for weightedBergman spaces. 相似文献
20.
Let (Xn,dn) be a sequence of finite metric spaces of uniformlybounded diameter. An equivalence relation D on the product defined by if and only if is a c0-equality.A systematic study is made of c0-equalities and Borel reductionsbetween them. Necessary and sufficient conditions, expressedin terms of combinatorial properties of metrics dn, are obtainedfor a c0-equality to be effectively reducible to the isomorphismrelation of countable structures. It is proved that every Borelequivalence relation E reducible to a c0-equality D either reducesa c0-equality D' additively reducible to D, or is Borel-reducibleto the equality relation on countable sets of reals. An appropriatelydefined sequence of metrics provides a c0-equality which isa turbulent orbit equivalence relation with no minimum turbulentequivalence relation reducible to it. This answers a questionof Hjorth. It is also shown that, whenever E is an F-equivalencerelation and D is a c0-equality, every Borel equivalence relationreducible to both D and to E has to be essentially countable.2000 Mathematics Subject Classification: 03E15. 相似文献