Showing papers on "Bicyclic semigroup published in 1996"
Journal Article•
TL;DR: In this article, it was shown that if G satisfies an algebraic condition, which is true for all abelian semigroups, then there exists a K-quasiconformal homeomorphism of U onto an open set V such that all the functions in G are meromorphic functions of V into itself.
Abstract: Let G be a semigroup of K-quasiregular or K-quasimeromorphic functions map- ping a given open set U in the Riemann sphere into itself, for a fixed K, the semigroup operation being the composition of functions. We prove that if G satisfies an algebraic condition, which is true for all abelian semigroups, then there exists a K-quasiconformal homeomorphism of U onto an open set V such that all the functions in f ◦G◦f −1 are meromorphic functions of V into itself. In particular, if U is the whole sphere then the elements of f ◦G ◦f −1 are rational functions. We give an example of a semigroup generated by two functions on the sphere, each quasiconformally conjugate to a quadratic polynomial, that cannot be quasiconformally conjugated to a semigroup of rational functions. We give another such example of a semigroup of K-quasiconformal homeo- morphisms. These results extend and complement a similar positive conjugacy result of Tukia and of Sullivan for groups of K-quasiconformal homeomorphisms.
37 citations
TL;DR: In this paper, it is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of this semigroup is investigated.
Abstract: It is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of this semigroup is investigated. The group constituents of this Clifford semigroup are exactly the quotients of totally ordered complete abelian groups, modulo dense subgroups. A characterization of these groups is obtained, and some realization results are proved when the skeleton of the totally ordered group is given.
31 citations
27 citations
TL;DR: The question if there exist semigroups containing both strong and non-strong magnifying elements was recently raised up by K.D. Magill and F. Catino as discussed by the authors.
Abstract: The question if there exist semigroups containing both strong and nonstrong magnifying elements was recently raised up by K.D. Magill Jr. in [3] and by F. Catino and F. Migliorini in [1]. In this note we give an affirmative answer to this question.
18 citations
TL;DR: It is shown that every regular unambiguous semigroup is isomorphic to an iterative Morita semigroup of a special form by relying on Morita theory.
Abstract: In recent work we associated a natural category to a semigroup and developed Morita theory for semigroups. In particular we gave a generalisation of Rees’ Theorem which led us to define what we call a Morita semigroup, this is our analogue of a structure matrix semigroup. In this article we formulate a method for extending Morita semigroups by groups. We say that a semigroup is an iterative Morita semigroup if it is obtained by successive applications of pasting families of Morita semigroups which have been extended by groups. By relying on Morita theory we show that every regular unambiguous semigroup is isomorphic to an iterative Morita semigroup of a special form. Our result can be viewed as a co-ordinate free version of the Synthesis Theorem.
17 citations
12 citations
TL;DR: The authors generalize the classical Munn representation of an inverse semigroup with the introduction of what they call ordered representations of inverse semigroups, which are examples of the Wagner-Preston representation and effective actions of O'Carroll and McAlister.
9 citations
TL;DR: In this paper, the notions of causal paths and causal homotopies were introduced for certain basic constructions in (Lie) semigroup theory, and the major result is the construction in this causal context of an analogue of the universal covering semigroup and the demonstration that local homomorphisms on the given semigroup extend to global homomorphism on it.
Abstract: We introduce the notions of causal paths and causal homotopies, modifications of the traditional notions of paths and homotopies, as more suitable for certain basic constructions in (Lie) semigroup theory. The major result is the construction in this causal context of an analogue of the universal covering semigroup and the demonstration that local homomorphisms on the given semigroup extend to global homomorphisms on it. In certain important cases, it is shown that this semigroup actually agrees with the universal covering semigroup.
9 citations
TL;DR: It is proved that a finitely presented Rees quotient of a free inverse semigroup has polynomial or exponential growth, and that the type of growth is algorithmically recognizable.
Abstract: We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial or exponential growth, and that the type of growth is algorithmically recognizable. We prove that such a semigroup has polynomial growth if and only if it satisfies a certain semigroup identity. However we give an example of such a semigroup which has exponential growth and satisfies some nontrivial identity in signature with involution.
9 citations
TL;DR: In this paper, the authors studied the unit group U(ZS) of the integral semigroup ring ZS of a finite semigroup S. Throughout, they assumed that ZS has an identity, and unless mentioned otherwise, it is assumed that QS is a semisimple Artinian ring.
TL;DR: In this article, the fundamental double four-spiral semigroup (DSP4) was introduced as a building block of bisimple, idempotent-generated regular semigroups.
Abstract: We give a new description of the fundamental double four-spiral semigroup. The fundamental four-spiral semigroup Sp4 and the fundamental double fourspiral semigroup DSp4 were introduced in [1], [3], and [4]. These semigroups are interesting examples of fundamental regular semigroups, and are indispensable building blocks of bisimple, idempotent-generated regular semigroups. Their basic properties are recalled in parts 1 and 2 of this note. In part 3 we give an alternate construction ofDSp4 in terms of the free semigroup on two generators, as a set of quadruples with a simple, bicyclic-like multiplication. This permits shorter proofs and easier access to the main properties of DSp4 :d escriptions of DSp4=L and DSp4=R (part 4); reduced form of the elements (part 5); and the property of congruencesC6Lthat DSp4=C is completely simple (part 6).
TL;DR: In this article, conditions for a congruence on a general semigroup (with E(S) a subsemigroup, resp.) are given, which ensure that Lallement's result holds.
Abstract: G. Lallement [5] proved that every idem potent congruence class of a regular semigroup contains an idem potent. P. Edwards [4] generalized this property of congruences to eventually regular semigroups. Using the natural partial order of the semigroup (see [6]) a weakened version of this result will be proved for the more general class of E-inversive semigroups. But for particular congruences the original result of Lallement still holds for every E-inversive semigroup. Finally, conditions for a congruence on a general semigroup (with E(S) a subsemigroup, resp.) are given, which ensure that Lallement's result holds.
TL;DR: One-parameter semigroups occurring in operator-limit distributions are investigated in this article, where the topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.
Abstract: One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.
01 Jan 1996
TL;DR: In this paper, it was shown that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup, and that the semigroup algebra of every linear cancellation semigroup is semisimple.
Abstract: We consider algebras over a field of characteristic zero, and prove that the Jacobson radical is homogeneous in every algebra graded by a linear cancellative semigroup. It follows that the semigroup algebra of every linear cancellative semigroup is semisimple. © 1996 American Mathematical Society.
01 Jan 1996
TL;DR: In this article, the semigroup structure of the syntactic monoid Syn(C+) of a maximal prefix code C+ is investigated and it is shown that Syn has a kernel J which is a right group.
Abstract: In this paper we investigate the semigroup structure of the syntactic monoid Syn(C+) of C+, the semigroup generated by a maximal prefix code C for which C+ is a single class of the syntactic congruence. In particular we prove that for such a prefix code C, either Syn(C+) is a group or it is isomorphic to a special type of submonoid of G× T (R) where G is a group and T (R) is the full transformation semigroup on a set R with more than one element. From this description we conclude that Syn(C+) has a kernel J which is a right group. We further investigate separately the case when J is a right zero semigroup and the case when J is a group.
TL;DR: It is shown that (if the class is non-empty) it has a ‘greatest’ member ∈S which is in a sense the free completely 0-simple semigroup on S, and described how the other members can be obtained as homomorphic images of .
Abstract: In this paper we investigate the class of all completely 0-simple semigroups of left quotients of a given semigroup S. We show that (if the class is non-empty) it has a ‘greatest’ member ∈S which is in a sense the free completely 0-simple semigroup on S, and describe how the other members can be obtained as homomorphic images of .
TL;DR: In this paper, it was shown that a semigroup ring R [S ] has the 2-generator property for large classes of commutative cancellative semigroups.
TL;DR: In this article, a semigroup model of social networks is presented, where data matrices representing the perceived relationships between members of a social network are used to construct a (possibly infinite) data semigroup of derived relations defined by real matrix multiplication.
Abstract: This paper addresses the development of a semigroup model of social networks. Data matrices which represent the perceived relationships between members of a social network are used to construct a (possibly infinite) data semigroup of derived relations defined by (real) matrix multiplication. This complex structure is analyzed by forming interaction semigroups. These semigroups are homomorphic images of the data semigroup. The corresponding congruences are generated by identifying products of finite order which are highly positively correlated. Several methods of generating the interaction semigroups are examined and are shown to generate nonhomomorphic semigroups. For each congruence, an associated triple of numbers can be defined which may serve as an indicator of the validity and/or a measure of the stability of the semigroup model. A series of hypothetical examples is developed to study how the algebraic properties of interaction semigroups reflect and uncover properties of associated networks. Specifi...
TL;DR: In this paper, the authors present a structure theorem for solid binary algebras in terms of semilattices and rectangular bands, and also show that a free solid binary algebra can be embedded in a free completely regular semigroup.
Abstract: A solid binary algebra in an abstract characterisation of the idempotents of a completely regular semigroup. We present here a structure theorem for solid binary algebras in terms of semilattices and rectangular bands. We also show that a free solid binary algebra can be embedded in a free completely regular semigroup; thus the word problem for the free solid binary algebra can be solved by using a solution of the word problem for the free completely regular semigroup.
TL;DR: In this paper, the inverse semigroups of bicongruences of a given algebra form are defined, and conditions on the structure semilattices, rectangular band components, and linking homomorphisms of two normal bands with isomorphic inverse semi-groups are given.
01 Jan 1996
TL;DR: In this paper, the basic theory of continuous one-parameter semigroups from two different points of view is discussed and explained from a mathematical point of view, which can be considered as providing an abstract framework for the solution of evolution equations.
Abstract: In these lectures we discuss and explain the basic theory of continuous one-parameter semigroups from two different points of view. The semigroups can be considered as providing an abstract framework for the solution of evolution equations which will be described at greater length in the lectures of Ecker and Urbas or as providing the basic elements of the functional calculus to be developed in the lectures of Albrecht, Duong and Mcintosh.