Showing papers on "Bicyclic semigroup published in 1999"
TL;DR: In this paper, a topological analogue of the Abramov-Rokhlin formula for a free semigroup action is proposed, in which a skew-product transformation whose fiber entropy is taken to be the entropy of the initial action is considered.
Abstract: A definition of topological entropy for a free semigroup action is suggested. Suppose that a free semigroup acts on a compact metric space by continuous self-maps. To this action, we assign a skew-product transformation whose fiber entropy is taken to be the entropy of the initial action. The main result is Theorem 1, a topological analogue of the Abramov–Rokhlin formula.
56 citations
TL;DR: In this article, a semigroup F E that plays for a class of E -semi-adequate semigroups is presented, where F E is an inverse semigroup with semilattice of idempotents.
50 citations
01 Oct 1999
TL;DR: In this article, the McAlister structure theory was generalized to O-E-unitary inverse semigroups with a pure prehomomorphism to a primitive inverse semigroup.
Abstract: This is the first of three papers in which we generalise the classical McAlister structure theory for £-unitaryinverse semigroups to those O-E-unitary inverse semigroups which admit a O-restricted, idempotent pureprehomomorphism to a primitive inverse semigroup. In this paper, we concentrate on finding necessary andsufficient conditions for the existence of such prehomomorphisms in the case of 0-£-unitary inverse monoids.A class of inverse monoids which satisfy our conditions automatically are those which are unambiguousexcept at zero, such as the polycyclic monoids.1991 Mathematics subject classification: 20M18 (18B40).
48 citations
TL;DR: In this paper, a new category of Banach algebras, l 1 -Munn algeses, is introduced, which is used as a tool in the study of semigroup algebras.
37 citations
TL;DR: The theory of inverse semigroups as discussed by the authors is a refinement of the Wagner-Preston representation theorem, which states that every inverse semigroup is isomorphic to an inverse monoid of some structure.
31 citations
TL;DR: In this paper, a semigroup is locally testable if it is k-testable for some k > 0, where k is the number of subwords of length k of the words a and b. The structure of local testable semigroups is studied and sufficient conditions for local testability are given.
Abstract: Let S be a semigroup of words over an alphabet ∑ . Suppose tliar every two words u and e over ∑ are equal in S if (1) the sets of subwords of length k of the words a and b coincide and are non-empty. (2) the prefix (suffix) of u of length k1 is equal to the prefix (suffix) of e. Then S is called k-testable. A semigroup is locally testable if it is k-testable for some k > 0. We present a finite basis of identities of the variety of A'-testable semigroups. The structure of k-testable semigroup is studied. Necessarv and sufficient conditions for local testability will be given. A solution to one problem from the survey of Shevrin and Sukhanov (1985) will be presented.
17 citations
TL;DR: In this article, the ideals and Green's relations on such semigroups were described, and the congruences on certain Rees factor semigroup were constructed for finite and one-to-one partial transformations.
Abstract: In 1987 Sullivan determined the elements of the semigroup N ( X ) generated by all nilpotent partial transformations of an infinite set X ; and later in 1997 he studied subsemigroups of N ( X ) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and Green's relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X . We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.
11 citations
TL;DR: A Rees congruence semigroup is a semigroup for which every non-identity Congruence is a ReesCongruence as discussed by the authors. But this semigroup does not hold for finite chains.
Abstract: A Rees congruence semigroup is one for which every non-identity congruence is a Rees congruence. We show that the widely studied semigroup of endomorphisms of a finite chain is a Rees congruence semigroup.
11 citations
TL;DR: In this paper, it was shown that the Mal'cev semigroup identity xn = yn holds in the circle semigroup of an associative algebra over an infinite field precisely when the algebra is Lie nilpotent of class at most n.
Abstract: We show that the Mal'cev semigroup identity xn = yn holds in the circle semigroup of an associative algebra over an infinite field precisely when the algebra is Lie nilpotent of class at most n. The Mal'cev semigroup law xn = yn holds in a group if and only if the group is nilpotent of class at most n.
11 citations
TL;DR: Conditions (i) and (ii) are found to be sufficient for a commutative semigroup with identity and satisfying some other conditions to be a fuzzy multiplication semigroup.
9 citations
TL;DR: In this article, the authors characterised all non-degenerate homomorphisms from the multiplicative semigroup of all 2×2 matrices over an arbitrary field to the semigroup of 3×3 matrices on the same field.
TL;DR: In this article, the existence of an identity in these semigroups in terms of the Lie structure of R was shown to be equivalent to R being upper Lie nilpotent.
Abstract: Denote by (R,.) the multiplicative semigroup of an associative algebra R over an infinite field, and let (R,*) represent R when viewed as a semigroup via the circle operation x*y=x+y+xy. In this paper we characterize the existence of an identity in these semigroups in terms of the Lie structure of R. Namely, we prove that the following conditions on R are equivalent: the semigroup (R,*) satisfies an identity; the semigroup (R,.) satisfies a reduced identity; and, the associated Lie algebra of R satisfies the Engel condition. When R is finitely generated these conditions are each equivalent to R being upper Lie nilpotent.
TL;DR: In this article, the authors determine the compatible partial orders on the bicyclic semigroup B which turn it into a semilatticed semigroup, and they show that these are the only compatible orderings which turn B into a lattice ordered semigroup.
Abstract: In this paper we determine those compatible partial orders on the bicyclic semigroup B which turn it into a semilatticed semigroup. We shall see that there are exactly four distinct compatible total orderings on B. These are the only compatible orderings which turn B into a lattice ordered semigroup. On a group every compatible semilattice ordering is a lattice ordering. However this is not the case with inverse semigroups. Indeed, the situation regarding semilattice orderings on the bicyclic semigroups is much richer. There are four infinite families of compatible semilattce orderings on B. Two of these families turn B into a V-semilatticed semigroup; two of the families turn it into a ^-semilatticed semigroup.
TL;DR: In this paper, the authors give procedures for determining whether a given monoid is an affine semigroup and for computing the dual of a semigroup, and also give methods for deciding whether an affined semigroup is normal and/or full.
TL;DR: In this paper, it was shown that the adjoint semigroup of a p-separable BCI-algebra is a direct product of a negatively partially ordered semigroup and an abelian group.
Abstract: We give some conditions under which the p-semisimple part SP(X) of a BCIalgebra X becomes an ideal, and prove that the adjoint semigroup of a p-separable BCI-algebra is a direct product of a negatively partially ordered semigroup and an abelian group.
TL;DR: In this paper, lower-order perturbations of a symmetric second-order differential operator were studied for generating a hypercontractive semigroup, and it was shown that the perturbed semigroup is also hyper-contractive under some exponential integrability conditions on the coefficients.
Abstract: In this paper, we study lower order perturbations of a symmetric second-order differential operator generating a hypercontractive semigroup. We give a probabilistic representation of the, in general, not sub-Markovian semigroup associated with the perturbed operator and prove that the perturbed semigroup is also hypercontractive under some exponential integrability conditions on the coefficients.
TL;DR: In this paper, the minimal quantum dynamical semigroup on a von Neumann algebra is constructed and a set of necessary and sufficient conditions for the conservativity of the minimal semigroup is given.
Abstract: Given a formal unbounded generator, the minimal quantum dynamical semigroup on a von Neumann algebra is constructed. A set of equivalent necessary and sufficient conditions for the conservativity of the minimal semigroup is given and in the case when it is not conservative, a distinguished family of conservative perturbations of the semigroup is studied. Finally, some of these results are applied to the classical Markov semigroup with arbitrary state space.
TL;DR: In this paper, the explicit construction of a 0-simple Rees matrix semigroup is suggested such that the lattice of left annihilators of this semiigroup is isomorphic to L.
Abstract: the explicit construction of a 0-simple Rees matrix semigroup is suggested such that the lattice of left annihilators of this semigroup is isomorphic to L.
TL;DR: The concept of column tight Rees matrix semigroups was introduced in this article. But the concept of a column tight matrix semigroup has not yet been studied in this paper.
Abstract: For the translational hulls of two Rees matrix semigroups represented by means of matrices, we construct all their isomorphisms again in matrix form. These are matrices of arbitrary size over a group with zero satisfying certain conditions on nonzero entries. We introduce the concept of a r-maximal completely 0-simple and of a Rees matrix semigroup. To this end, we construct a Rees matrix semigroup from a group and a nonempty set and introduce the concept of a column tight Rees matrix semigroup. We study these concepts in relation to the translational hull of a Rees matrix semigroup.
TL;DR: In this article, the authors apply the theory of inductive groupoids, in particular the construction of the idempotent generated regular semigroup given in §6 of [8] to detemine some combinatorial properties of the semigroup Sn.
Abstract: be a vector space of dimension n over a field K. Here we denote by Sn the set of all singular endomorphisms of V. Erdos [5], Dawlings [4] and Thomas J. Laffey [6] have shown that Sn is an idempotent generated regular semigroup. In this paper we apply the theory of inductive groupoids, in particular the construction of the idempotent generated regular semigroup given in §6 of [8] to detemine some combinatorial properties of the semigroup Sn.
Journal Article•
TL;DR: In this article, the authors generalize some algebraic properties known to hold for the additive semigroup of the integers to the case of the Stone-Cech compactification of a semigroup with an operation which is continous only in one variable.
Abstract: be an infinite, discrete, cancellative semigroup and let BetaS be the Stone-Cech compactification of S. Then BetaS is a semigroup with an operation which extends that of S and which is continous only in one variable. We generalize some algebraic properties known to hold for the additive semigroup of the integers.
01 Jul 1999
Abstract: This paper contains an attempt to discuss some properties of relations induced by translations, including distribution of idempotents. We will begin with start two equivalence relations, give some results to be used frequently and show a distribution of idempotents. In fact it will be shown in ” l.Introduction and Preliminaries” that the two relations are relations including Green’s relations. Using the relations, we will discuss idempotents which behave as left or right identities in equivalence classes induced by the relations. In the last section, as an application of the properties of idempotent and a semigroup extended by translations shown here, some special class of semigroups, abundand semigroups, will be discussed, which is closely related with the distribution of idempotents.
01 Jan 1999
TL;DR: In this paper, the minimal quantum dynamical semigroup on a von Neumann algebra is constructed and a set of necessary and sufficient conditions for the conservativity of the minimal semigroup is given.
Abstract: Given a formal unbounded generator, the minimal quantum dynamical semigroup on a von Neumann algebra is constructed. A set of equivalent necessary and sufficient conditions for the conservativity of the minimal semigroup is given and in the case when it is not conservative, a distinguished family of conservative perturbations of the semigroup is studied. Finally, some of these results are applied to the classical Markov semigroup with arbitrary state space.
01 Jul 1999
01 Nov 1999
TL;DR: In this paper, the authors consider almost periodic type function algebras on a weighted semitopological semigroup, and define their corresponding weighted semigroup compactifications, and show that these compactifications do not retain all the nice properties of the ordinary semi-group compactifications unless they impose some restrictions on the weight functions.
Abstract: We consider some almost periodic type function algebras on a weighted semitopological semigroup, and using the set of multiplicative means on each of these algebras, we define their corresponding weighted semigroup compactifications. This will constitute an effective tool for investigating the properties of the function algebras concerned. We also show that these compactifications do not retain all the nice properties of the ordinary semigroup compactifications unless we impose some restrictions on the weight functions.