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2.
In this paper we develop a very basic method to classify ( J, σ)-irreducible monoids of type A 4. As a typical example, we list all the types for the monoids corresponding to the strongly dominant weights. This example also shows that there is no general theorem to determine the cross-section lattices for reductive monoids according to their Dynkin diagrams as Putcha and Renner’s recipe for J-irreducible monoids. 相似文献
3.
In this paper we study several structural properties of the monoids \poi
n
of all injective order preserving partial transformations on a chain with n elements. Our main aim is to give a presentation for these monoids.
January 27, 1999 相似文献
4.
Hedrlín and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M . In this paper we give a construction G( M) for a graph with prescribed endomorphism monoid M . Using this construction we derive bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. For example we show that for every monoid M , | M |= m there is a graph G with End( G)? M and | E( G)|≤(1 + 0(1)) m2. This is, up to a factor of 1/2, best possible since there are monoids requiring a graph with \begin{eqnarray*} && \frac{m^{2}}{2}(1 -0(1)) \end{eqnarray*} edges. We state bounds for the class of all monoids as well as for certain subclasses—groups, k‐cancellative monoids, commutative 3‐nilpotent monoids, rectangular groups and completely simple monoids. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 241–262, 2009 相似文献
5.
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
6.
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
7.
By a regular act we mean an act such that all its cyclic subacts are projective. In this paper we introduce strong ( P)-cyclic property of acts over monoids which is an extension of regularity and give a classification of monoids by this property
of their right (Rees factor) acts. 相似文献
8.
We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids indicate that they should give origin to new knot algebras; indeed, our tied monoids include the tied braid monoid and the tied singular braid monoid, which were used, respectively, to construct new polynomial invariants for classical links and singular links. Consequently, we provide a mechanism to attach an algebra to each tied monoid; this mechanism not only captures known generalizations of the bt-algebra, but also produces possible new knot algebras. To build the tied monoids it is necessary to have presentations of set partition monoids of types A, B and D, among others. For type A we use a presentation due to FitzGerald and for the other type it was necessary to built them. 相似文献
9.
The purpose of this article is to introduce the theory of presentations of monoids acts. We aim to construct “nice” general presentations for various act constructions pertaining to subacts and Rees quotients. More precisely, given an M-act A and a subact B of A, on the one hand, we construct presentations for B and the Rees quotient A/ B using a presentation for A, and on the other hand, we derive a presentation for A from presentations for B and A/ B. We also construct a general presentation for the union of two subacts. From our general presentations, we deduce a number of finite presentability results. Finally, we consider the case where a subact B has a finite complement in an M-act A. We show that if M is a finitely generated monoid and B is finitely presented, then A is finitely presented. We also show that if M belongs to a wide class of monoids, including all finitely presented monoids, then the converse also holds. 相似文献
10.
We shall call a monoid S principally weakly (weakly) left coherent if direct products of nonempty families of principally weakly (weakly) flat right S-acts are principally weakly (weakly) flat. Such monoids have not been studied in general. However, Bulman-Fleming and McDowell proved that a commutative monoid S is (weakly) coherent if and only if the act S I is weakly flat for each nonempty set I. In this article we introduce the notion of finite (principal) weak flatness for characterizing (principally) weakly left coherent monoids. Also we investigate monoids over which direct products of acts transfer an arbitrary flatness property to their components. 相似文献
11.
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 R 1 and R 2 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
12.
Hypersubstitutions are mappings which map operation symbols to terms of the corresponding arities. They were introduced as a way of making precise the concept of a hyperidentity and generalizations to M-hyperidentities. A variety in which every identity is satisfied as a hyperidentity is called solid. If every identity is an M-hyperidentity for a subset M of the set of all hypersubstitutions, the variety is called M-solid. There is a Galois connection between monoids of hypersubstitutions and sublattices of the lattice of all varieties of algebras of a given type. Therefore, it is interesting and useful to know how semigroup or monoid properties of monoids of hypersubstitutions transfer under this Galois connection to properties of the corresponding lattices of M-solid varieties. In this paper, we study the order of each hypersubstitution of type (2, 2), i.e., the order of the cyclic subsemigroup generated by that hypersubstitution of the monoid of all hypersubstitutions of type (2, 2). The main result is that the order is 1, 2, 3, 4 or infinite. 相似文献
14.
This work is devoted to results obtained in the model theory of regular polygons. We give a characterization of monoids with
axiomatizable and model-complete class of regular polygons. We describe monoids with complete class of regular polygons that
satisfy some additional conditions. We study monoids whose regular core is represented as a union of finitely many principal
right ideals and all regular polygons over which have a stable and superstable theory. We prove the stability of the class
of all regular polygons over a monoid provided this class is axiomatizable and model-complete. We also describe monoids for
which the class of all regular polygons is superstable and ω-stable provided this class is axiomatizable and model-complete.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 107–157, 2004. 相似文献
16.
Abstract. We introduce the class of localizable monoids. It contains inverse monoids. Then we define localizations of monoids with
respect to localizable submonoids of their monoid of endomorphisms. These constructions can be applied to a category of left
modules or to a category of A -rings. As a result, we are able to invert endomorphisms within the original category, unlike inversive localizations of
Cohn's type which need a base change. 相似文献
17.
There has recently been considerable interest in inverse monoids which are presented by generators and relations. In this
work the author employs graphical techniques to investigate the word problem for presentations of inverse monoids which generalize
the case in which all relations in a presentation are of the form w=w
2
. The work also investigates free objects in finitely based varieties of inverse semigroups, where the free objects have similar
presentations. A fundamental charecteristic of the monoids (semigroups) investigated is: if F is a free inverse monoid and M=F/θ, then for m∈F, the R-class of mθ has no more elements than the R-class of m. 相似文献
18.
This article considers those monoids S satisfying one or both of the finitary properties ( R) and ( r), focussing for the most part on inverse monoids. These properties arise from questions of axiomatisability of classes of S-acts, and appear to be of interest in their own right. If S is weakly right noetherian (WRN), that is, S has the ascending chain condition on right ideals, then certainly ( r) holds. Other than this, we show that ( R), ( r), and (WRN) are independent. Our most detailed results are for Clifford monoids, in which case we completely characterise those S with trivial structure homomorphisms satisfying ( R) or ( r). 相似文献
19.
In this paper we compute the abelian kernels of the monoids POIn and POPIn of all injective order preserving and respectively, orientation preserving, partial transformations on a chain with n elements. As an application, we show that the pseudovariety POPI generated by the monoids POPIn ( n epsilon N) is not contained in the Mal'cev product of the pseudovariety POI generated by the monoids POIn ( n epsilon N) with the pseudovariety Ab of all finite abelian groups. 相似文献
20.
In (Bull. Lond. Math. Soc. 33:385–390, 2001) Bican, Bashir and Enochs finally solved a long standing conjecture in module theory that all modules over a unitary ring
have a flat cover. The only substantial work on covers of acts over monoids seems to be that of Isbell (Semigroup Forum 2:95–118,
1971), Fountain (Proc. Edinb. Math. Soc. (2) 20:87–93, 1976) and Kilp (Semigroup Forum 53:225–229, 1996) who only consider projective covers. To our knowledge the situation for flat covers of acts has not been addressed and this
paper is an attempt to initiate such a study. We consider almost exclusively covers of cyclic acts and restrict our attention
to strongly flat and condition ( P) covers. We give a necessary and sufficient condition for the existence of such covers and for a monoid to have the property that
all its cyclic right acts have a strongly flat cover (resp. ( P)-cover). We give numerous classes of monoids that satisfy these conditions and we also show that there are monoids that do
not satisfy this condition in the strongly flat case. We give a new necessary and sufficient condition for a cyclic act to
have a projective cover and provide a new proof of one of Isbell’s classic results concerning projective covers. We show also
that condition ( P) covers are not unique, unlike the situation for projective covers. 相似文献
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