共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper we investigate under which conditions a monoid R is defined by the endomorphism monoid of an act over R. More
precisely, we ask when an isomorphism between two such endomorphism monoids over monoids R1 and R2 is induced by a semilinear isomorphism. The question is considered also for ordered and for topological monoids. On the way
we characterize monoids over which all projective acts are free. An abstract of this paper appeared in the Proceedings of
the Conference on Semigroups, Szeged 1972. 相似文献
2.
It is proved that the fixed point submonoid and the periodic point submonoid of a trace monoid endomorphism are always finitely generated. If the dependence alphabet is a transitive forest, it is proved that the set of regular fixed points of the (Scott) continuous extension of an endomorphism to real traces is Ω-rational for every endomorphism if and only if the monoid is a free product of free commutative monoids. 相似文献
3.
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
4.
Perfect monoids revisited 总被引:1,自引:0,他引:1
Mati Kilp 《Semigroup Forum》1996,53(1):225-229
A new characterization of perfect monoids, i.e., monoids over which every act has a projective cover, is given. As was shown
by Fountain [1] a monoid is perfect if and only if all strongly flat acts over it are projective. Using our new condition,
an alternative version is given of a recent result, of Liu [7] describing monoids over which all strongly flat right acts
are projective generators, or are free.
This research has been supported by the Estonian Science Foundation, Grant No. 930.
I would like to thank the School of Mathematical and Computational Sciences of the University of St. Andrews for excellent
working conditions. 相似文献
5.
Andrew Solomon 《Semigroup Forum》1996,53(1):351-368
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
6.
Yurii V. Zhuchok 《Algebra Universalis》2016,76(3):355-366
We describe all endomorphisms of a free trioid of rank 1 and construct a semigroup which is isomorphic to the endomorphism monoid of such free trioid. Also, we give an abstract characteristic for the endomorphism monoid of a free trioid of rank 1 and prove that free trioids are determined by their endomorphism monoids. 相似文献
7.
The constant mappings onto the unit form a zero subcategory of any category of monoid homomorphisms; a varietyV of monoids isalmost universal if every category of algebras is isomorphic to a class of all nonzero homomorphisms between members ofV. Almost universal monoid varieties are shown to be exactly those varieties containing all commutative monoids in which the identity xnyn=(xy)n fails for every n>1. Almost universal varieties of monoids can also be characterized categorically as the varieties containing all groups with zero as one-object full subcategories.Presented by B. M. Schein.The support of NSERC is gratefully acknowledged. 相似文献
8.
In this paper ordered wreath products of ordered monoids by ordered acts are investigated. In 4. we characterize idempotent isotone wreath products. In 3. the monoid of order preserving endomorphisms of a free ordered act is represented as Cartesian ordered isotone wreath product. Moreover, we give conditions for this wreath product to be I-regular. 相似文献
9.
《Journal of Pure and Applied Algebra》2023,227(1):107161
We introduce a ramified monoid, attached to each Brauer–type monoid, that is, to the symmetric group, to the Jones and Brauer monoids among others. Ramified monoids correspond to a class of tied monoids arising from knot theory and are interesting in themselves. The ramified monoid attached to the symmetric group is the Coxeter-like version of the so–called tied braid monoid. We give a presentation of the ramified monoid attached to the Brauer monoid. Also, we introduce and study two tied-like monoids that cannot be described as ramified monoids. However, these monoids can also be regarded as tied versions of the Jones and Brauer monoids. 相似文献
10.
Hailong Hou 《Discrete Mathematics》2008,308(17):3888-3896
In this paper, we give several approaches to construct new End-regular (-orthodox) graphs by means of the join and the lexicographic product of two graphs with certain conditions. In particular, the join of two connected bipartite graphs with a regular (orthodox) endomorphism monoid is explicitly described. 相似文献
11.
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.
12.
Presentations are found for the wreath product of two monoids, the Schützenberger product of two monoids, the Bruck-Reilly extension of a monoid, strong semilattices of monoids and Rees matrix semigroups of monoids. 相似文献
13.
Let X be a graph, S End X be its strong endomorphism monoid. It is proved that S End X is a regular monoid if and only if the canonical strong factor graph U of X contains no proper subgraph which is isomorphic to U. The result generalizes that of U. Knauer about the regularity of strong endomorphism monoids of graphs. 相似文献
14.
In this paper, we study the atomic structure of Puiseux monoids generated by monotone sequences. To understand this atomic structure, it is often useful to know whether the monoid has a bounded generating set. We provide necessary and sufficient conditions for the atomicity and boundedness to be transferred from a monotone Puiseux monoid to all its submonoids. Finally, we present two special subfamilies of monotone Puiseux monoids and fully classify their atomic structure. 相似文献
15.
16.
We obtain presentations for the Brauer monoid, the partial analogue of the Brauer monoid, and for the greatest factorizable
inverse submonoid of the dual symmetric inverse monoid. In all three cases we apply the same approach, based on the realization
of all these monoids as Brauer-type monoids. 相似文献
17.
Margolis and Meakin use the Cayley graph of a group presentation to construct E-unitary inverse monoids [11]. This is the technique we refer to as graph expansion. In this paper we consider graph expansions of unipotent monoids, where a monoid is unipotent if it contains a unique idempotent. The monoids arising in this way are E-unitary and belong to the quasivariety of weakly left ample monoids. We give a number of examples of such monoids. We show that the least unipotent congruence on a weakly left ample monoid is given by the same formula as that for the least group congruence on an inverse monoid and we investigate the notion of proper for weakly left ample monoids. Using graph expansions we construct a functor Fe from the category U of unipotent monoids to the category PWLA of proper weakly left ample monoids. The functor Fe is an expansion in the sense of Birget and Rhodes [2]. If we equip proper weakly left ample monoids with an extra unary operation and denote the corresponding category by PWLA 0 then regarded as a functor U→PWLA 0 Fe is a left adjoint of the functor Fσ : PWLA 0 → U that takes a proper weakly left ample monoid to its greatest unipotent image. Our main result uses the covering theorem of [8] to construct free weakly left ample monoids. 相似文献
18.
We relate the old and new cohomology monoids of an arbitrary monoid M with coefficients in semimodules over M, introduced in the author’s previous papers, to monoid and group extensions. More precisely, the old and new second cohomology monoids describe Schreier extensions of semimodules by monoids, and the new third cohomology monoid is related to a certain group extension problem. 相似文献
19.
It is proved that the universal group of a torsion free rigid monoid is torsion free. As a consequence, a new condition on a monoid M for the monoid ring R[M] to be a 2-fir is given. Furthermore, the monoids between a rigid monoid and its universal group are studied. 相似文献
20.
Ulrich Knauer 《Semigroup Forum》1971,3(1):359-370
In this paper we shall consider a non-additive category of A-modules, that is, instead of a ring A we take a monoid A which
acts on sets from the left. These objects will be called A-acts. We investigate indecomposable A-acts and generators and characterize
projectives in this category. For a given monoid A we describe all monoids B such that the category of B-acts is equivalent
to the category of A-acts. In particular we find that equivalence of these categories yields an isomorphism between the monoids
A and B if A is a group or finite or commutative. This differs from the additive case where the categories of modules over
a commutative field and its ring of nxn matrices are equivalent. Finally we give examples of non-isomorphic monoids A and
B such that the corresponding categories are equivalent. 相似文献