共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper gives decidable conditions for when a finitely generated subgroup of a free group is the fundamental group of a Schützenberger automaton corresponding to a monoid presentation of an inverse monoid. Also, generalizations are given to specific types of inverse monoids as well as to monoids which are "nearly inverse." This result has applications to computing membership for inverse monoids in a Mal'cev product of the pseudovariety of semilattices with a pseudovariety of groups. This paper also shows that there is a bijection between strongly connected inverse automata and subgroups of a free group, generated by positive words. Hence, we also obtain that it is decidable whether a finite strongly connected inverse automaton is a Schützenberger automaton corresponding to a monoid presentation of an inverse monoid. Again, we have generalizations to other types of inverse monoids and to "nearly inverse" monoids. We show that it is undecidable whether a finite strongly connected inverse automaton is a Schützenberger automaton of a monoid presentation of an E-unitary inverse monoid. 相似文献
3.
In this article we characterize monoids over which every right S-act has a strongly flat (condition (P)) cover. Similar to the perfect monoids, such monoids are characterized by condition (A) and having strongly flat (condition (P)) cover for each cyclic right S-act. We also give a new characterization for perfect monoids as monoids over which every strongly flat right S-act has a projective cover. 相似文献
5.
We discuss residual finiteness and several related separability conditions for the class of monoid acts, namely weak subact separability, strong subact separability and complete separability. For each of these four separability conditions, we investigate which monoids have the property that all their (finitely generated) acts satisfy the condition. In particular, we prove that: all acts over a finite monoid are completely separable (and hence satisfy the other three separability conditions); all finitely generated acts over a finitely generated commutative monoid are residually finite and strongly subact separable (and hence weakly subact separable); all acts over a commutative idempotent monoid are residually finite and strongly subact separable; and all acts over a Clifford monoid are strongly subact separable. 相似文献
6.
We investigate a notion of soficity for monoids. A group is sofic as a group if and only if it is sofic as a monoid. All finite monoids, all commutative monoids, all free monoids, all cancellative one-sided amenable monoids, all multiplicative monoids of matrices over a field, and all monoids obtained by adjoining an identity element to a semigroup are sofic. On the other hand, although the question of the existence of a non-sofic group remains open, we prove that the bicyclic monoid is not sofic. This shows that there exist finitely presented amenable inverse monoids that are non-sofic. 相似文献
7.
本文研究图及其强自同态幺半群.首先刻画了图的强自同态幺半群的正则元,然后给出了此幺半群正则的充要条件.这推广了[1]和[2]中关于有限图的强自同态幺半群正则的结果. 相似文献
8.
In this paper we pursue the study of the decidability of the dot-depth hierarchy. We give an effective lower bound for the dotdepth of an aperiodic monoid. The main tool for this is the study of a certain operation on varieties of finite monoids in terms of Mal'cev product. We also prove the equality of two decidable varieties which were known to contain all dot-depth two monoids. Finally, we restrict our attention to inverse monoids, and we prove that the class of inverse dot-depth two monoids is locally finite. 相似文献
9.
We present an example of two countable ω-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids—in other words, no isomorphism between these monoids is a homeomorphism. For the same two structures, the automorphism groups and polymorphism clones are isomorphic, but not topologically isomorphic. In particular, there exists a countable ω-categorical structure in a finite relational language which can neither be reconstructed up to first-order biinterpretations from its automorphism group, nor up to existential positive bi-interpretations from its endomorphism monoid, nor up to primitive positive bi-interpretations from its polymorphism clone. 相似文献
10.
This paper continues the study of a class of inverse monoids, called Tarski monoids, that can be regarded as non-commutative generalizations of the unique countable, atomless Boolean algebra. These inverse monoids are related to a class of étale topological groupoids under a non-commutative generalization of classical Stone duality and, significantly, they arise naturally in the theory of dynamical systems as developed by Matui. We are thereby able to reinterpret a theorem of Matui (à la Rubin) on a class of étale groupoids as an equivalent theorem about a class of Tarski monoids: two simple Tarski monoids are isomorphic if and only if their groups of units are isomorphic. The inverse monoids in question may also be viewed as countably infinite generalizations of finite symmetric inverse monoids. Their groups of units therefore generalize the finite symmetric groups and include amongst their number the Thompson groups \(V_{n}\). 相似文献
11.
It is shown that the graph product of automatic monoids is always automatic thereby improving on a result by Veloso da Costa
[22] who showed this result provided the factors have finite geometric type. Secondly, we prove that, in general, the free
product (and therefore the graph product) of biautomatic monoids need not be biautomatic. Imposing a restriction on the factors
that is symmetric to Veloso da Costa's "finite geometric type", the biautomaticity of all graph products of biautomatic monoids
is shown. 相似文献
12.
The Möbius inversion formula, introduced during the 19th century in number theory, was generalized to a wide class of monoids called locally finite such as the free partially commutative, plactic and hypoplactic monoids for instance. In this contribution are developed and used some topological and algebraic notions for monoids with zero, similar to ordinary objects such as the (total) algebra of a monoid, the augmentation ideal or the star operation on proper series. The main concern is to extend the study of the Möbius function to some monoids with zero, i.e., with an absorbing element, in particular the so-called Rees quotients of locally finite monoids. Some relations between the Möbius functions of a monoid and its Rees quotient are also provided. 相似文献
13.
An odd Sugihara monoid is a residuated distributive lattice-ordered commutative idempotent monoid with an order-reversing involution that fixes the monoid identity. The main theorem of this paper establishes a category equivalence between odd Sugihara monoids and relative Stone algebras. In combination with known results, it swiftly determines which varieties of odd Sugihara monoids are [strongly] amalgamable and which have the strong [or weak] epimorphism-surjectivity property. In particular, the full variety is shown to have all of these properties. The results extend, with slight modification, to the case where the algebras are bounded. Logical applications include immediate answers to some questions about projective and finite Beth definability and interpolation in the uninorm-based logic IUML, its boundless fragment and all of their extensions. 相似文献
14.
Semigroup Forum - This is a survey on factorization theory. We discuss finitely generated monoids (including affine monoids), primary monoids (including numerical monoids), power sets with set... 相似文献
15.
Transfer Krull monoids are a recently introduced class of monoids and include the multiplicative monoids of all commutative Krull domains as well as of wide classes of non-commutative Dedekind domains. We show that transfer Krull monoids are fully elastic (i.e., every rational number between 1 and the elasticity of the monoid can be realized as the elasticity of an element). In commutative Krull monoids which have sufficiently many prime divisors in all classes of their class group, the set of catenary degrees and the set of tame degrees are intervals. Without the assumption on the distribution of prime divisors, arbitrary finite sets can be realized as sets of catenary degrees and as sets of tame degrees. 相似文献
16.
We investigate the generation of factorizable inverse monoids, paying special attention to the factorizable parts of the symmetric
and dual symmetric inverse monoids. Key ideas covered include rank, relative rank, Sierpiński rank, and the semigroup Bergman
property. The results for finite monoids are well-known or follow quickly from well-known facts, so most of the paper concerns
the infinite case. 相似文献
17.
In this paper Morita duality for monoids is introduced. Necessary and sufficient conditions for two monoids S and T to be
Morita dual are given. Moreover, it is shown that if S and T are Morita dual monoids, then S and U are Morita dual if and
only if T and U are Morita equivalent. In addition, every finite monoid having Morita duality is selfdual and even reflexive. 相似文献
18.
The pseudovariety DA consists of all aperiodic finite monoids all of whose regular -classes are subsemigroups (that is, rectangular subbands); this pseudovariety appears quite frequently in various contexts in finite semigroup theory. In this note we prove that all its members have a log-polynomial free spectrum, thereby making a new step towards proving the Seif conjecture on the dichotomy of free spectra of finite monoids. 相似文献
20.
The Catalan monoid and partial Catalan monoid of a directed graph are introduced. Also introduced is the notion of a local endomorphism of a tree, and it is shown that the Catalan (resp. partial Catalan) monoid of a tree is simply its monoid of extensive local endomorphisms (resp. partial endomorphisms) of finite shift. The main results of this paper are presentations for the Catalan and partial Catalan monoids of a tree. Our presentation for the Catalan monoid of a tree is used to give an alternative proof for a result of Higgins. We also identify results of Aîzen?tat and Popova which give presentations for the Catalan monoid and partial Catalan monoid of a finite symmetric chain. 相似文献
|