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1.
Elton Pasku 《Semigroup Forum》2011,83(1):75-88
We prove that the category of Clifford semigroups and prehomomorphisms CSP\mathcal{CSP} is isomorphic to a certain subcategory of the category of diagrams over groups. Under this isomorphism, Clifford semigroups
are identified with certain functors. As an application of the isomorphism theorem, we show that the category with objects
commutative inverse semigroups having the same semilattice of idempotents and with morphisms, the inverse semigroup homomorphisms
that fix the semilattice, imbeds into a category of right modules over a certain ring. Also we find a very close relationship
between the cohomology groups of a commutative inverse monoid and the cohomology groups of the colimit group of the functor
giving the monoid. 相似文献
2.
The left regular band structure on a hyperplane arrangement and its representation theory provide an important connection between semigroup theory and algebraic combinatorics. A finite semigroup embeds in a real hyperplane face monoid if and only if it is in the quasivariety generated by the monoid obtained by adjoining an identity to the two-element left zero semigroup. We prove that this quasivariety is on the one hand polynomial time decidable, and on the other minimally non-finitely based. A similar result is obtained for the semigroups embeddable in complex hyperplane semigroups. 相似文献
3.
G. Mashevitzky Boris M. Schein 《Proceedings of the American Mathematical Society》2003,131(6):1655-1660
We determine all isomorphisms between the endomorphism semigroups of free monoids or free semigroups and prove that automorphisms of the endomorphism semigroup of a free monoid or a free semigroup are inner or ``mirror inner". In particular, we answer a question of B. I. Plotkin.
4.
The aim of this paper is to study a class of strong Dubreil-Jacotin
semigroups, so-called split integral Dubreil-Jacotin semigroups.
We establish the structure of split integral
Dubreil-Jacotin semigroups in terms of the cartesian ordered
semidirect product of an ordered monoid and an ordered group.
Also, the lexicographic ordered semidirect product is considered.
These results extend main results in [1]. 相似文献
5.
We show, contrary to some published statements, that spectral synthesis does not generally hold for commutative semigroups that are not groups. On the positive side we prove that it holds if the semigroup is a monoid with no prime ideal. For semigroups with a prime ideal, the picture is not so clear. On the negative side we provide a variety of examples illustrating the failure of spectral synthesis for many semigroups with prime ideals, but we also give examples of semigroups with prime ideals on which spectral synthesis holds.
相似文献6.
《数学学报(英文版)》2015,(7)
A semigroup is called completely J~((e))-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid.It is proved that completely J~((e))-simple semigroups form a quasivarr ity.Moreover,the construction of free completely J~((e))-simple semigroups is given.It is found that a free completely J~((e))-simple semigroup is just a free completely J~*-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
7.
Kwok Wai Lau 《代数通讯》2013,41(7):2617-2629
The generators of the Temperley-Lieb algebra generate a monoid with an appealing geometric representation. It has been much studied, notably by Louis Kauffman. Borisavljevi?, Do?en, and Petri? gave a complete proof of its abstract presentation by generators and relations, and suggested the name “Kauffman monoid”. We bring the theory of semigroups to the study of a certain finite homomorphic image of the Kauffman monoid. We show the homomorphic image (the Jones monoid) to be a combinatorial and regular *-semigroup with linearly ordered ideals. The Kauffman monoid is explicitly described in terms of the Jones monoid and a purely combinatorial numerical function. We use this to describe the ideal structure of the Kauffman monoid and two other of its homomorphic images. 相似文献
8.
Free completely <Emphasis Type="Italic">J</Emphasis><Superscript>(<Emphasis Type="Italic">ℓ</Emphasis>)</Superscript>-simple Semigroups 下载免费PDF全文
A semigroup is called completely J(ι)-simple if it is isomorphic to some Rees matrix semigroup over a left cancellative monoid and each entry of whose sandwich matrix is in the group of units of the left cancellative monoid. It is proved that completely J(ι)-simple semigroups form a quasivarity. Moreover, the construction of free completely J(ι)-simple semigroups is given. It is found that a free completely J(ι)-simple semigroup is just a free completely J *-simple semigroup and also a full subsemigroup of some completely simple semigroups. 相似文献
9.
Marcel Jackson 《Semigroup Forum》2002,64(2):297-324
We show how to construct all ``forbidden divisors' for the pseudovariety of not inherently nonfinitely based finite semigroups. Several other results concerning finite semigroups that generate an inherently
nonfinitely based variety that is miminal amongst those generated by finite semigroups are obtained along the way. For example,
aside from the variety generated by the well known six element Brandt monoid \tb , a variety of this type is necessarily generated by a semigroup with at least 56 elements (all such semigroups with 56 elements
are described by the main result).
September 23, 1999 相似文献
10.
We consider the question of membership of A ∨ G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion
for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A ∨ G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; we remark
that any finite monoid with semilattice of idempotents is weakly abundant. To study such semigroups we develop a number of
techniques that may be of interest in their own right. 相似文献
11.
We describe all minimal noncryptic periodic semigroup [monoid] varieties. We
prove that there are exactly three distinct maximal cryptic semigroup [monoid] varieties contained in the variety determined
by xn ≈ x n+m, n ≥ 2, m ≥ 2. Analogous results are obtained for pseudovarieties: there are exactly three maximal cryptic pseudovarieties
of semigroups [monoids]. It is shown that if a cryptic variety or pseudovariety of monoids contains a nonabelian group, then
it consists of bands of groups only. Several characterizations are given of the cryptic overcommutative semigroup [monoid]
varieties. 相似文献
12.
The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups
that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal.
After considering various general properties that relate the imposed order to the natural order, we highlight the situation
in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine
the structure of a naturally ordered regular semigroup with an inverse monoid transversal. 相似文献
13.
14.
The rank of a semigroup is the cardinality of a smallest generating set. In this paper we compute the rank of the endomorphism
monoid of a non-trivial uniform partition of a finite set, that is, the semigroup of those transformations of a finite set
that leave a non-trivial uniform partition invariant. That involves proving that the rank of a wreath product of two symmetric
groups is two and then use the fact that the endomorphism monoid of a partition is isomorphic to a wreath product of two full
transformation semigroups. The calculation of the rank of these semigroups solves an open question. 相似文献
15.
《代数通讯》2013,41(6):2447-2459
The aim of this paper is to study a class of rpp semigroups, namely the perfect rpp semigroups. We obtain some characterization theorems for such semigroups. In particular, the spined product structure of perfect rpp semigroups is established. As an application of spined product structure, we prove that a perfect rpp semigroup is a strong semilattice of left cancellative planks. By a left cancellative plank, we mean a product of a left cancellative monoid and a rectangular band. Thus, the work of J.B. Fountain on C-rpp semigroups is further developed. 相似文献
16.
Theodore G. Faticoni 《代数通讯》2013,41(1):451-464
In this paper we present a division theorem for the pseudovariety of semigroups OP generated by all semigroups of orientation preserving full transformations on a finite chain, which is achieved by using a natural representation of a certain monoid of transformations of a set X as a monoid of transformations of a subset of X. 相似文献
17.
Peter Mayr 《Semigroup Forum》2013,86(3):613-633
An algebraic structure is finitely related (has finite degree) if its term functions are determined by some finite set of finitary relations. We show that the following finite semigroups are finitely related: commutative semigroups, 3-nilpotent monoids, regular bands, semigroups with a single idempotent, and Clifford semigroups. Further we provide the first example of a semigroup that is not finitely related: the 6-element Brandt monoid. This answers a question by Davey, Jackson, Pitkethly, and Szabó from Davey et al. (Semigroup Forum, 83(1):89–122, 2011). 相似文献
18.
19.
We study some aspects of Schein’s theory of cosets for closed inverse subsemigroups of inverse semigroups. We establish an index formula for chains of subsemigroups, and an analogue of M. Hall’s Theorem on the number of cosets of a fixed finite index. We then investigate the relationships between the following properties of a closed inverse submonoid of an inverse monoid: having finite index; being a recognizable subset; being a rational subset; being finitely generated (as a closed inverse submonoid). A remarkable result of Margolis and Meakin shows that these properties are equivalent for a closed inverse submonoid of a free inverse monoid. 相似文献
20.
本文首先研究了具有可消模断面的拟恰当半群的结构,然后给出了用可消模断面的拟恰当半群构造具有CO-恰当断面富足半群的方法. 相似文献