共查询到20条相似文献,搜索用时 78 毫秒
1.
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
2.
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
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.
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
5.
6.
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
7.
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
8.
Y. Chen 《Semigroup Forum》2001,62(1):41-52
9.
10.
I. S. Ponizovskii 《Journal of Mathematical Sciences》1990,52(3):3170-3178
The semigroup algebras over a field K of the semigroups Tn of all permutations of a set of n elements are considered. It is proved: if n≤3 and (n!)-1∈ K then the algebra KTn has a finite representation type. Also the finiteness of the representation type of the semigroup algebra KS is established,
where S is the sub-semigroup of Tn (n is arbitrary) such that S=Jn∪G where Jn={x∈Tn|rank x=1}, while G is a doubly transitive subgroup of the symmetric group Sn, the order of G being invertible in K.
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR,
Vol. 160, pp. 229–238, 1987. 相似文献
11.
Benjamin Steinberg 《Algebras and Representation Theory》2016,19(3):731-747
The representation theory of the symmetric group has been intensively studied for over 100 years and is one of the gems of modern mathematics. The full transformation monoid \(\mathfrak {T}_{n}\) (the monoid of all self-maps of an n-element set) is the monoid analogue of the symmetric group. The investigation of its representation theory was begun by Hewitt and Zuckerman in 1957. Its character table was computed by Putcha in 1996 and its representation type was determined in a series of papers by Ponizovski?, Putcha and Ringel between 1987 and 2000. From their work, one can deduce that the global dimension of \(\mathbb {C}\mathfrak {T}_{n}\) is n?1 for n = 1, 2, 3, 4. We prove in this paper that the global dimension is n?1 for all n ≥ 1 and, moreover, we provide an explicit minimal projective resolution of the trivial module of length n?1. In an appendix with V. Mazorchuk we compute the indecomposable tilting modules of \(\mathbb {C}\mathfrak T_{n}\) with respect to Putcha’s quasi-hereditary structure and the Ringel dual (up to Morita equivalence). 相似文献
12.
Kenneth R. Davidson 《Journal of Functional Analysis》2005,224(1):160-191
We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra An. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to a *-extendible representation σ. A *-extendible representation of An is regular if the absolutely continuous part coincides with the type L part. All known examples are regular. Absolutely continuous functionals are intimately related to maps which intertwine a given *-extendible representation with the left regular representation. A simple application of these ideas extends reflexivity and hyper-reflexivity results. Moreover the use of absolute continuity is a crucial device for establishing a density theorem which states that the unit ball of σ(An) is weak-* dense in the unit ball of the associated free semigroup algebra if and only if σ is regular. We provide some explicit constructions related to the density theorem for specific representations. A notion of singular functionals is also defined, and every functional decomposes in a canonical way into the sum of its absolutely continuous and singular parts. 相似文献
13.
An algebra A has finite degree if its term functions are determined by some finite set of finitary relations on A. We study this concept for finite algebras in general and for finite semigroups in particular. For example, we show that
every finite nilpotent semigroup has finite degree (more generally, every finite algebra with bounded p
n
-sequence), and every finite commutative semigroup has finite degree. We give an example of a five-element unary semigroup
that has infinite degree. We also give examples to show that finite degree is not preserved in general under taking subalgebras,
homomorphic images, direct products or subdirect factors. 相似文献
14.
Jeek and Kepka [4] proved that a universal algebra A with at least one at
least binary operation is isomorphic to the factor of a subdirectly irreducible algebra B by
its monolith if and only if the intersection of all of its (nonempty) ideals is nonempty, and
that B may be chosen to be finite if A is finite.
(By an ideal of A is meant a non-empty
subset I of A such that
f(a1, . . . ,
an) I whenever
f is an n-ary fundamental operation
of A and a1, . . . ,
an A are elements
with ai I for at
least one index i.) In the present
paper, we prove that if A is a semigroup, then B may be
chosen also to be a semigroup, but that a finite semigroup need not be isomorphic to the factor of a finite subdirectly
irreducible semigroup by its monolith. 相似文献
15.
P-Ehresmann semigroups are introduced by Jones as a common generalization of Ehresmann semigroups and regular \(*\)-semigroups. Ehresmann semigroups and their semigroup algebras are investigated by many authors in literature. In particular, Stein shows that under some finiteness condition, the semigroup algebra of an Ehresmann semigroup with a left (or right) restriction condition is isomorphic to the category algebra of the corresponding Ehresmann category. In this paper, we generalize this result to P-Ehresmann semigroups. More precisely, we show that for a left (or right) P-restriction locally Ehresmann P-Ehresmann semigroup \(\mathbf{S}\), if its projection set is principally finite, then we can give an algebra isomorphism between the semigroup algebra of \(\mathbf{S}\) and the partial semigroup algebra of the associate partial semigroup of \(\mathbf{S}\). Some interpretations and necessary examples are also provided to show why the above isomorphism dose not work for more general P-Ehresmann semigroups. 相似文献
16.
For any finite commutative idempotent semigroup S, a semilattice, we show how to compute the amenability constant of its semigroup algebra ℓ
1(S). This amenability constant is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices.
We also give example of a commutative Clifford semigroups G
n
whose semigroup algebras ℓ
1(G
n
) admit amenability constants of the form 41+4(n−1)/n. We also show there is no commutative semigroup whose semigroup algebra has an amenability constant between 5 and 9.
N. Spronk’s research was supported by NSERC Grant 312515-05. 相似文献
17.
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
18.
Changchang Xi 《Advances in Mathematics》2002,168(2):193-212
We study Auslander's representation dimension of Artin algebras, which is by definition the minimal projective dimension of coherent functors on modules which are both generators and cogenerators. We show the following statements: (1) if an Artin algebra A is stably hereditary, then the representation dimension of A is at most 3. (2) If two Artin algebras are stably equivalent of Morita type, then they have the same representation dimension. Particularly, if two self-injective algebras are derived equivalent, then they have the same representation dimension. (3) Any incidence algebra of a finite partially ordered set over a field has finite representation dimension. Moreover, we use results on quasi-hereditary algebras to show that (4) the Auslander algebra of a Nakayama algebra has finite representation dimension. 相似文献
19.
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
20.
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