共查询到20条相似文献,搜索用时 31 毫秒
1.
Y. Chen 《Semigroup Forum》2001,62(1):41-52
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For a left type-A monoid S , let tau be the congruence on S generated by R* . There exists a congruence rho on S which induces the least right cancellative congruence on each of the tau -classes. In this paper we investigate the congruence rho and give a structure theorem for the class of all left-type-A monoids for which rho intersection R* is the identity relation. 相似文献
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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
4.
Let S be an inverse semigroup and rho an idempotent separating congruence on S . It is proved that S can be embedded into a lambda-semidirect product of a group F by S /rho where F belongs to the variety generated by the idempotent classes of rho. 相似文献
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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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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
8.
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
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John R. Stembridge 《Annals of Combinatorics》2001,5(2):113-121
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Gejza Jenča 《Algebra Universalis》2002,48(4):399-411
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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
13.
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
14.
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
15.
Monoids for Which Condition (P) Acts are Projective 总被引:1,自引:0,他引:1
James Renshaw 《Semigroup Forum》2000,61(1):46-56
A characterisation of monoids for which all right S -acts satisfying conditions (P) are projective is given. We also give a new characterisation of those monoids for which all cyclic right S -acts satisfying condition (P) are projective, similar in nature to recent work by Kilp [6]. In addition we give a sufficient condition for all right S -acts that satisfy condition (P) to be strongly flat and show that the indecomposable acts that satisfy condition (P) are the locally cyclic acts. 相似文献
16.
Ivo Babu?ka 《Numerische Mathematik》2000,85(2):219-255
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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
18.
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
19.
M. Filali 《Semigroup Forum》1999,58(2):241-247
Let S be an infinite, discrete, cancellative semigroup and let BetaS be the Stone-Cech compactification of S . Then BetaS is a semigroup with an operation which extends that of S and which is continous only in one variable. We generalize some algebraic properties known to hold for the additive semigroup of the integers. 相似文献
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