Showing papers on "Bicyclic semigroup published in 2002"
TL;DR: In this article, all endomorphisms of the (finite) Brauer semigroup, its partial analogue and the semigroup of all partitions of a -element set are described.
Abstract: We describe all endomorphisms of the (finite) Brauer semigroup, its partial analogue and the semigroup of all partitions of a -element set.
41 citations
TL;DR: The contribution of profinite methods and the way they enriched and modified finite semigroup theory are surveyed.
Abstract: Many recent results in finite semigroup theory make use of profinite methods, that is, they rely on the study of certain infinite, compact semigroups which arise as projective limits of finite semigroups. These ideas were introduced in semigroup theory in the 1980s, first to describe pseudovarieties in terms of so-called pseudo-identities: this is Reiterman's theorem, which can be viewed as the (much more complex) finite algebra analogue of Birkhoff's variety theorem. Soon, these methods were used in conjunction with virtually all the other approaches of finite semigroups, notably to study the decidability of product pseudovarieties. This paper surveys the contribution of profinite methods and the way they enriched and modified finite semigroup theory.
41 citations
TL;DR: In this paper, the authors consider a Rees matrix semigroup S = M[U; I, J; P] over a semigroup U, with I and J finite index sets, and show that if S is an automatic semigroup and there is an entry p in the matrix P such that pU 1 = U then U is automatic.
Abstract: We consider a Rees matrix semigroup S = M[U; I, J; P] over a semigroup U, with I and J finite index sets, and relate the automaticity of S with the automaticity of U. We prove that if U is an automatic semigroup and S is finitely generated then S is an automatic semigroup. If S is an automatic semigroup and there is an entry p in the matrix P such that pU 1 = U then U is automatic. We also prove that if S is a prefix-automatic semigroup, then U is a prefix-automatic semigroup.
22 citations
20 citations
TL;DR: In this paper, the cardinality of minimal presentations for semigroups with minimal Apery set is derived for simplicial affine semigroup ring associated to a simplicial semigroup.
Abstract: We give an arithmetic characterization which allow us to determine algorithmically when the semigroup ring associated to a simplicial affine semigroup is Buchsbaum. This characterization is based on a test performed on the Apery sets of the extremal rays of the semigroup. We use this method to obtain the cardinality of minimal presentations for semigroups with minimal Apery set.
18 citations
TL;DR: In this article, the authors consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them, and show that they can be used to obtain a semigroup of the form
Abstract: We consider three operators which appear naturally in convexity theory and determine completely the structure of the semigroup generated by them.
18 citations
TL;DR: This paper obtains an inverse monoid theoretic condition for a subgroup to be quasiconvex allowing semigroup theoretic variants on the usual proofs that the intersection of such subgroups is quasiconsvex and that such sub groups are finitely generated.
Abstract: This paper explores various connections between combinatorial group theory, semigroup theory, and formal language theory. Let G = be a group presentation and ℬA, R its standard 2-complex. Suppose X is a 2-complex with a morphism to ℬA, R which restricts to an immersion on the 1-skeleton. Then we associate an inverse monoid to X which algebraically encodes topological properties of the morphism. Applications are given to separability properties of groups. We also associate an inverse monoid M(A, R) to the presentation with the property that pointed subgraphs of covers of ℬA, R are classified by closed inverse submonoids of M(A, R). In particular, we obtain an inverse monoid theoretic condition for a subgroup to be quasiconvex allowing semigroup theoretic variants on the usual proofs that the intersection of such subgroups is quasiconvex and that such subgroups are finitely generated. Generalizations are given to non-geodesic combings. We also obtain a formal language theoretic equivalence to quasiconvexity which holds even for groups which are not hyperbolic. Finally, we illustrate some applications of separability properties of relatively free groups to finite semigroup theory. In particular, we can deduce the decidability of various semidirect and Mal/cev products of pseudovarieties of monoids with equational pseudovarieties of nilpotent groups and with the pseudovariety of metabelian groups.
16 citations
TL;DR: In this paper, an irreducible multiplicative semigroup of non-negative square-zero operators acting on L p ≥ 0, 1 for 1 ≤ p < ∞ was constructed.
Abstract: We construct an irreducible multiplicative semigroup of non-negative square-zero operators acting onL
p
[0,1), for 1≤p<∞.
13 citations
TL;DR: In this article, the authors give a necessary and sufficient condition for a monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.
Abstract: It is known that for any finite group G given by a finite group presentation \(\) there exists a finite semigroup presentation \(\) for G of the same deficiency, i.e. satisfying \(\). It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and sufficient condition for a finite monoid M, given by a finite monoid presentation, to have a finite semigroup presentation of the same deficiency.
9 citations
TL;DR: In this paper, the authors studied non-degenerate irreducible homomorphisms from the multiplicative semigroup of all 2-by-2 complex matrices to the matrix conjugation.
TL;DR: It is shown that idempotents can be replaced by projections when one passes from regular to *-regular semigroup congruences, and it is proved that an appropriate equivalence on the set of projections and all elements equivalent to projections fully suffice to reconstruct an (involution-preserving) congruence of a *- regular semigroup.
Abstract: In this paper we study the congruences of *-regular semigroups, involution semigroups in which every element is p-related to a projection (an idempotent fixed by the involution). The class of *-regular semigroups was introduced by Drazin in 1979, as the involutorial counterpart of regular semigroups. In the standard approach to *-regular semigroup congruences, one ,starts with idempotents, i.e. with traces and kernels in the underlying regular semigroup, builds congruences of that semigroup, and filters those congruences which preserve the involution. Our approach, however, is more evenhanded with respect to the fundamental operations of *-regular semigroups. We show that idempotents can be replaced by projections when one passes from regular to *-regular semigroup congruences. Following the trace-kernel balanced view of Pastijn and Petrich, we prove that an appropriate equivalence on the set of projections (the *-trace) and the set of all elements equivalent to projections (the *-kernel) fully suffice to reconstruct an (involution-preserving) congruence of a *-regular semigroup. Also, we obtain some conclusions about the lattice of congruences of a *-regular semigroup.
TL;DR: In this paper, it was shown that no algorithm can determine from an arbitrary recursive system of semigroup identities whether the variety defined by this system is finitely based, i.e., it is not finitely-based.
Abstract: No algorithm determines from an arbitrary recursive system of semigroup identities whether the variety defined by this system is finitely based.
TL;DR: In this paper, the authors determine some forms of the relations in a finite semigroup presentation with zero deficiency which does or does not define a group and conclude that a finite Rees matrix semigroup M[G; I, Λ; P] is efficient when G is efficient and the index sets I, ǫ are finite.
Abstract: The purpose of this paper is twofold. First we determine some forms of the relations in a finite semigroup presentation with zero deficiency which does or does not define a group. Moreover, we conclude that a finite Rees matrix semigroup M[G; I, Λ; P] is efficient when G is efficient and the index sets I, Λ are finite.
TL;DR: It is proved that the link semigroup is isomorphic to some algebraically defined semigroup with a simple system of relations, which means knot theory is represented as a bracket calculus: the link recognition problem is reduced to a recognition problem in this semigroup.
Abstract: In this paper, we introduce a way of encoding links (long links). This ways leads to a combinatorial representation of links by words in a given finite alphabet. We prove that the link semigroup is isomorphic to some algebraically defined semigroup with a simple system of relations. Thus, knot theory is represented as a bracket calculus: the link recognition problem is reduced to a recognition problem in this semigroup.
TL;DR: The study of OPn, the monoids of orientation-preserving mappings on a chain, is continued, leading to the study of the semigroup pseudovariety O, showing among other results that it is self-dual and contains all commutative semigroups.
Abstract: We continue the study of OPn, the monoids of orientation-preserving mappings on a chain, leading to the study of the semigroup pseudovariety generated by all monoids OPn, showing among other results that is self-dual and contains all commutative semigroups.
TL;DR: In this article, the authors studied Noetherian local subrings of, such that, and with nonzero conductor, i.e., rings of the form, where are polynomials (or power series).
Abstract: We study Noetherian local subrings of , such that , and with nonzero conductor , i.e., rings of the form , where are polynomials (or power series). For every such ring, is a numerical semigroup. Let be a numerical semigroup. Then is called a semigroup ring if for some . is called monomial if each ring with value semigroup is a semigroup ring. We discuss this and some related concepts.
01 Jan 2002
TL;DR: In this paper, a finite combinatorial inverse semigroup of moderate size is presented, such that the lattice of all subvarieties of this semigroup has the cardinality of the continuum.
Abstract: A finite combinatorial inverse semigroup of moderate size is
presented such that the variety of combinatorial inverse
semigroups generated by this semigroup posseses the following
properties. The lattice of all subvarieties of this variety has
the cardinality of the continuum. Moreover, the mentioned
semigroup, and hence also the variety it generates and its
subvarieties, all have E-unitary covers over any non-trivial
variety of groups.
TL;DR: In this article, the theory of Lawson for 0 -bisimple inverse monoids was generalized to wider classes of 0 -bisimple regular semigroups, and a necessary and sufficient condition for a 0-bimple R-unipotent semigroup to admit a 0 -restricted idempotent pure prehomomorphism to a primitive inverse semigroup was given.
Abstract: We generalize theory of Lawson for 0 -bisimple inverse monoids to wider classes of 0 -bisimple regular semigroups. We give a necessary and sufficient condition for a 0 -bisimple R-unipotent semigroup to admit a 0-restricted idempotent-pure prehomomorphism to a primitive inverse semigroup. Several illustrations of the theory are obtained as an application of the results in this paper.
TL;DR: In this paper, the Frobenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ-finite regular measure is studied.
Abstract: We consider the Frobenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ-finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Frobenius-Perron semigroup of linear operators is C0-continuous in the space Lμ 1(X). We also give a geometrical condition which ensures C0-continuity of the Frobenius-Perron semigroup of linear operators in the space Lμ p(X) for 1≤pl∞, as well as in the space Lloc 1 .
TL;DR: In this paper, a finite combinatorial inverse semigroup Θ of moderate size is presented, such that the variety of the inverse semigroups generated by Θ possesses the following properties: the lattice of all subvarieties of this variety has the cardinality of the continuum.
Abstract: A finite combinatorial inverse semigroup Θ of moderate size is presented such that the variety of combinatorial inverse semigroups generated by Θ possesses the following properties. The lattice of all subvarieties of this variety has the cardinality of the continuum. Moreover, this semigroup Θ, and hence also the variety it generates and its subvarieties, all have E-unitary covers over any non-trivial variety of groups. This indicates that the mentioned uncountable sublattice appears quite near the bottom of the lattice of all varieties of combinatorial inverse semigroups.
TL;DR: In this article, a PO-sextet is defined and a structure of E-unitary regular semigroups is described, which is called PO-SEXTE.
Abstract: In this paper we define a concept of a PO-sextet and describe a structure of E-unitary regular semigroups.
TL;DR: In this paper, it was shown that the same implication holds for positive endo-morphisms, which map generators to positive words, also holds for semigroups, and that all implications for positive laws of length 1.
Abstract: 2. Let a semigroup — la bw impl a y a semigroup law u = v in groups. Doesthe same implication hold in semigroups?To show implication of laws in semigroups we can use only so-called positive endo-morphisms, which map generators to positive words. It is shown in [8] (an example atthe end of this paper), that all implications for positive laws of length ^ 5 which holdin groups, also are valid for semigroups. The fac
TL;DR: In this article, the necessary and sufficient condition for a locally inverse semigroup to be embeddable into a Rees matrix semigroup over a generalized inverse semi-composition is given.
Abstract: We give a necessary and sufficient condition for a locally inverse semigroup to be embeddable into a Rees matrix semigroup over a generalized inverse semigroup.
01 Jan 2002
TL;DR: In this paper, a PO-sextet is defined and a structure of E-unitary regular semigroups is described, based on the concept of Eunitary Regular Semigroups.
Abstract: In this paper we define a concept of a PO-sextet and describe a structure of E-unitaryregular semigroups.
Journal Article•
TL;DR: In this paper, it was proved that the localization of a regular semigroup S on the subsemigroupE(S) generated by its set of all idempotents E(S), is unique.
Abstract: It is proved that the localization of a regular semigroup S on the subsemigroupE(S)generated by its set of all idempotents E(S) exists and is unique.The smallest group congruence on a regular semigroup is also given.
BRAC1
TL;DR: In this article, the relation S defined by a monoid T and the Bruck semigroup B(T,α) over T was investigated by means of a (minimal) family Ϝ whose members can not appear as subsemigroups.
Abstract: The relation in the title is S defined by
$$a\mathcal{S}b \Leftrightarrow a^2 = ab = ba$$
on an arbitrary semigroup. We investigate antisymmetry of S by means of a (minimal) family Ϝ whose members can not appear as subsemigroups. Transitivity of S is characterized similarly by means of the family Ϝ and homomorphic images of a certain semigroup. We study the transfer of certain properties of a monoid T and the Bruck semigroup B(T,α) over T. The paper concludes with a consideration of certain properties of the relation S on inverse semigroups.
TL;DR: In this paper, it is shown that spectral synthesis for points on the real line is also provided by analytic semigroup techniques, and that Esterle's proof may also be adapted to provide Wiener theorem for some elementary hypergroups.
Abstract: In 1980, J. Esterle proved the Wiener theorem forL1 (—) by a completely new method using analytic semigroup techniques. We show here how to extend the method in two different ways. First, it is shown that spectral synthesis for points on the real line is also provided by analytic semigroup techniques. Second, Esterle's proof may also be adapted to provide Wiener theorem for some elementary hypergroups.