共查询到20条相似文献,搜索用时 31 毫秒
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.
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
3.
The Semigroup of Hall Matrices over Distributive Lattices 总被引:3,自引:0,他引:3
Yijia Tan 《Semigroup Forum》2000,61(2):303-314
In this paper, the semigroup Hn (L) of Hall matrices over a complete and completely distributive lattice L is studied. A Hall matrix is a matrix which is greater (for the order associated with the lattice structure) than an invertible matrix. Some necessary and sufficient conditions for a Hall matrix to be regular in the semigroup Hn (L) are given and Green's relations of the semigroup Hn (L) are described. Also, the sandwich semigroup of Hall matrices over the lattice L is studied. 相似文献
4.
A finite semigroup S is said to be efficient if it can be defined by a presentation (A | R) with |R | -|A |=rank(H 2 (S )). In this paper we demonstrate certain infinite classes of both efficient and inefficient semigroups. Thus, finite abelian groups, dihedral groups D 2 n with n even, and finite rectangular bands are efficient semigroups. By way of contrast we show that finite zero semigroups and free semilattices are never efficient. These results are compared with some well-known results on the efficiency of groups. 相似文献
5.
Y. Chen 《Semigroup Forum》2001,62(1):41-52
6.
C. M. Ringel 《Semigroup Forum》2000,61(3):429-434
Let Tn be the semigroup of all transformations of a set of n elements and k a field of characteristic 0. According to Ponizovskii, the semigroup algebra kTn is of finite representation type if n h 3. According to Putcha, kTn is of infinite representation type if n S 5. Here, we deal with the remaining case n =4 and show that kT 4 is also of finite representation type. Note that the quiver of kT 4 already has been exhibited by Putcha, here we determine the relations. It turns out that kT 4 is a string algebra and its global dimension is 3. 相似文献
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9.
K. Geetha 《Semigroup Forum》1999,58(2):207-221
Let V be a vector space of dimension n over a field K . Here we denote by Sn the set of all singular endomorphisms of V . Erdos [5], Dawlings [4] and Thomas J. Laffey [6] have shown that Sn is an idempotent generated regular semigroup. In this paper we apply the theory of inductive groupoids, in particular the construction of the idempotent generated regular semigroup given in §6 of [8] to detemine some combinatorial properties of the semigroup Sn . 相似文献
10.
Peer Christian Kunstmann 《Semigroup Forum》2000,60(2):310-320
We show that several spectral inclusions known for C 0 -semigroups fail for semigroups of closed operators, even if they can be regularized. We introduce the notion of spectral completeness for the regularizing operator C which implies equality of the spectrum and the C -spectrum of the generator. We prove spectral inclusions under this additional assumption. We give a series of examples in which the regularizing operator is spectrally complete including generators of integrated semigroups, of distribution semigroups, and of some semigroups that are strongly continuous for t > 0. 相似文献
11.
Claudio Gutiérrez 《Semigroup Forum》2000,61(1):154-158
Using techniques of Rewriting Theory, we present a new proof of the known theorem of Munn that FIX , the free inverse semigroup on X , is isomorphic to birooted word-trees on X . 相似文献
12.
A frame multiresolution (FMRA for short) orthogonalwavelet is a single-function orthogonal wavelet such that theassociated scaling space V 0 admits a normalized tight frame(under translations). In this article, we prove that for anyexpansive matrix A with integer entries, there existA -dilation FMRA orthogonal wavelets. FMRA orthogonal waveletsfor some other expansive matrix with non integer entries are also discussed. 相似文献
13.
An ordered pair (e,f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent.
Previously [1] we have established that there are four distinct types of skew pairs of idempotents. We have also described
(as quotient semigroups of certain regular Rees matrix semigroups [2]) the structure of the smallest regular semigroups that
contain precisely one skew pair of each of the four types, there being to within isomorphism ten such semigroups. These we
call the derived Rees matrix semigroups. In the particular case of full transformation semigroups we proved in [3] that TX contains all four skew pairs of idempotents if and only if |X| ≥ 6. Here we prove that TX contains all ten derived Rees matrix semigroups if and only if |X| ≥ 7. 相似文献
14.
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
15.
Gejza Jenča 《Algebra Universalis》2002,48(4):399-411
16.
Let S be a regular semigroup with set of idempotents E(S) . Given x,y ∈ S , we say that (x,y) is a skew pair if x y \notin E(S) whereas y x ∈ E(S) . Here we use this concept to characterise certain regular Rees matrix semigroups. 相似文献
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18.
T. Shibata 《Annales Henri Poincare》2001,2(4):713-732
19.
Esteban Andruchow 《Complex Analysis and Operator Theory》2016,10(6):1383-1409
An idempotent operator E in a Hilbert space \({\mathcal {H}}\) \((E^2=1)\) is written as a \(2\times 2\) matrix in terms of the orthogonal decomposition (R(E) is the range of E) as We study the sets of idempotents that one obtains when \(E_{1,2}:R(E)^\perp \rightarrow R(E)\) is a special type of operator: compact, Fredholm and injective with dense range, among others.
相似文献
$$\begin{aligned} {\mathcal {H}}=R(E)\oplus R(E)^\perp \end{aligned}$$
$$\begin{aligned} E=\left( \begin{array}{l@{\quad }l} 1_{R(E)} &{} E_{1,2} \\ 0 &{} 0 \end{array} \right) . \end{aligned}$$
20.
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