Addition theorems and representations of topological semigroups

Let a representation T of semigroup G on linear space X be given. We call x∈Xa finite vector if its orbit T(G) is contained in a finite-dimensional subspace. In this paper some statements on finite vectors will be proved and applied to functional equations

     

单的非负有序关联半群

一个负有序关联半群(S,≤,.,*)称为单的关联半群,如果S的所有滤子是{1}和S本身.对负有序关联半群是单的关联半群进行了刻画,给出了一个负的关联半群是单的关联半群的等价条件.     

On U-orthodox semigroups

As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semi-groups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in HU on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup WU and a V-ample semigroup ...     

Numerical semigroups and periodic orbits for Markov interval maps

Interval maps constitute a very important class of discrete dynamical systems with a well developed theory. Our purpose in this paper is to study a particular class of interval maps for which the set of periods is a numerical semigroup.     

The structure of superabundant semigroups

A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.     

Embedding the bicyclic semigroup into countably compact topological semigroups

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p,q). We prove that a topological semigroup S with pseudocompact square contains no dense copy of C(p,q). On the other hand, we construct a (consistent) example of a pseudocompact (countably compact) Tychonoff semigroup containing a copy of C(p,q).     

Global convoluted semigroups

Global exponentially bounded convoluted semigroups in Banach spaces are systematically treated with the help of Laplace transform. A perturbation theorem in this context is proved and some characterizations of the introduced class of analytic convoluted semigroups are obtained. Illustrative examples of generators of convoluted semigroups, including differential operators, are presented. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tensor products of recurrent hypercyclic semigroups

We study tensor products of strongly continuous semigroups on Banach spaces that satisfy the hypercyclicity criterion, the recurrent hypercyclicity criterion or are chaotic.     

Medial permutable semigroups of the first kind

We say that a semigroup S is a permutable semigroup if the congruences of S commute with each other, that is, α○β=β○α is satisfied for all congruences α and β of S. A semigroup is called a medial semigroup if it satisfies the identity axyb=ayxb. The medial permutable semigroups were examined in Proc. Coll. Math. Soc. János Bolyai, vol. 39, pp. 21–39 (1981), where the medial semigroups of the first, the second and the third kind were characterized, respectively. In Atta Accad. Sci. Torino, I-Cl. Sci. Fis. Mat. Nat. 117, 355–368 (1983) a construction was given for medial permutable semigroups of the second [the third] kind. In the present paper we give a construction for medial permutable semigroups of the first kind. We prove that they can be obtained from non-archimedean commutative permutable semigroups (which were characterized in Semigroup Forum 10, 55–66, 1975). Research supported by the Hungarian NFSR grant No T042481 and No T043034.     

Supercyclic and chaotic translation semigroups

We give a necessary and sufficient condition for a translation semigroup to be supercyclic and to be chaotic in a weighted function space.

     

On the Embedding of Ordered Semigroups into Ordered Group

It was shown in [7] that any right reversible, cancellative ordered semigroup can be embedded into an ordered group and as a consequence, it was shown that a commutative ordered semigroup can be embedded into an ordered group if and only if it is cancellative. In this paper we introduce the concept of L-maher and R-maher semigroups and use a technique similar to that used in [7] to show that any left reversible cancellative ordered L or R-maher semigroup can be embedded into an ordered group.     

A generalized Clifford theorem of semigroups

A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant.In 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups.Several years later,Fountain generalized this result to the class of superabundant semigroups.In this p...     

Tight representations of semilattices and inverse semigroups

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleanness present in the semilattice of idempotents of  . After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative. The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E ^*-unitaries. Partially supported by CNPq.     

On the total variation, topological entropy and sensitivity for interval maps

A concept related to total variation termed H₁ condition was recently proposed to characterize the chaotic behavior of an interval map f by Chen, Huang and Huang [G. Chen, T. Huang, Y. Huang, Chaotic behavior of interval maps and total variations of iterates, Internat. J. Bifur. Chaos 14 (2004) 2161-2186]. In this paper, we establish connections between H₁ condition, sensitivity and topological entropy for interval maps. First, we introduce a notion of restrictiveness of a piecewise-monotone continuous interval map. We then prove that H₁ condition of a piecewise-monotone continuous map implies the non-restrictiveness of the map. In addition, we also show that either H₁ condition or sensitivity then gives the positivity of the topological entropy of f.     

Soft ordered semigroups

Molodtsov introduced 1999 the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. In this paper we apply the notion of soft sets by Molodtsov to ordered semigroups. The notions of (trivial, whole) soft ordered semigroup, soft ordered subsemigroup, soft left (right) ideal, and left (right) idealistic soft ordered semigroup are introduced, and various related properties are investigated (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterization of some topological semigroups whose level curves are homothetic

We characterize all non-strict Archimedeant-norms whose level curves are homothetic.     

Proper extensions of weakly left ample semigroups

Summary We consider proper (idempotent pure) extensions of weakly left ample semigroups. These are extensions that are injective in each <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>\widetilde{\mathcal{R}}$-class. A graph expansion of a weakly left ample semigroup S is shown to be such an extension of S. Using semigroupoids acted upon by weakly left ample semigroups, we prove that any weakly left ample semigroup which is a proper extension of another such semigroup T is (2,1)-embeddable into a λ-semidirect product of a semilattice by T. Some known results, by O'Carroll, for idempotent pure extensions of inverse semigroups and, by Billhardt, for proper extensions of left ample semigroups follow from this more general situation.