scholarly journals GENERATORS OF REGULAR SEMIGROUPS

2008 ◽  
Vol 50 (1) ◽  
pp. 47-53
Author(s):  
SHMUEL KANTOROVITZ
Keyword(s):  
Regular Semigroup ◽  
Strong Operator Topology ◽  
Holomorphic Extension ◽  
Converse Theorem ◽  
Holomorphic Semigroup ◽  
Regular Semigroups ◽  
Strong Operator ◽  
Basic Facts ◽  
The Right ◽  
Holomorphic Extensions

AbstractA regular semigroup (cf. [4, p. 38]) is a C0-semigroup T(⋅) that has an extension as a holomorphic semigroup W(⋅) in the right halfplane $\Bbb C^+$, such that ||W(⋅)|| is bounded in the ‘unit rectangle’ Q:=(0, 1]× [−1, 1]. The important basic facts about a regular semigroup T(⋅) are: (i) it possesses a boundary groupU(⋅), defined as the limit lims → 0+W(s+i⋅) in the strong operator topology; (ii) U(⋅) is a C0-group, whose generator is iA, where A denotes the generator of T(⋅); and (iii) W(s+it)=T(s)U(t) for all s+it ∈$\Bbb C^+$ (cf. Theorems 17.9.1 and 17.9.2 in [3]). The following converse theorem is proved here. Let A be the generator of a C0-semigroup T(⋅). If iA generates a C0-group, U(⋅), then T(⋅) is a regular semigroup, and its holomorphic extension is given by (iii). This result is related to (but not included in) known results of Engel (cf. Theorem II.4.6 in [2]), Liu [7] and the author [6] for holomorphic extensions into arbitrary sectors, of C0-semigroups that are bounded in every proper subsector. The method of proof is also different from the method used in these references. Criteria for generators of regular semigroups follow as easy corollaries.

The Right Regular Representation of a Compact Right Topological Group

1998 ◽  
Vol 41 (4) ◽  
pp. 463-472 ◽  
Author(s):  
Alan Moran
Keyword(s):  
Topological Group ◽  
Representation Theory ◽  
Regular Representation ◽  
Strong Operator Topology ◽  
Topological Groups ◽  
Compact Topological Group ◽  
Strong Operator ◽  
Counter Example ◽  
The Right ◽  
Compact Right Topological Group

AbstractWe show that for certain compact right topological groups, , the strong operator topology closure of the image of the right regular representation of G in L(H), where H = L2(G), is a compact topological group and introduce a class of representations, R , which effectively transfers the representation theory of over to G. Amongst the groups for which this holds is the class of equicontinuous groups which have been studied by Ruppert in [10].We use familiar examples to illustrate these features of the theory and to provide a counter-example. Finally we remark that every equicontinuous group which is at the same time a Borel group is in fact a topological group.

Discourse

2016 ◽  
Author(s):  
Massimo Poesio
Keyword(s):  
Language Use ◽  
Structure Theory ◽  
Hierarchy Theory ◽  
Discourse Representation Theory ◽  
Theoretical Approaches ◽  
Discourse Model ◽  
Relational Coherence ◽  
Basic Facts ◽  
The Right ◽  
Intentional Structure

Discourse is the area of linguistics concerned with the aspects of language use that go beyond the sentence—and in particular, with the study of coherence and salience. In this chapter we present a few key theories of these phenomena. We distinguish between two main types of coherence: entity coherence, primarily established through anaphora; and relational coherence, expressed through connectives and other relational devices. Our discussion of anaphora and entity coherence covers the basic facts about anaphoric reference and introduces the dynamic approach to the semantics of anaphora implemented in theories such as Discourse Representation Theory, based on the notion of discourse model and its updates. With regards to relational coherence, we review some of the main claims about the relational structure of discourse—such as the claim that coherent discourses have a tree structure, or the right frontier hypothesis—and four main theoretical approaches: Rhetorical Structure Theory, Grosz and Sidner’s intentional structure theory, the inference-based approach developed by Hobbs and expanded in Segmented DRT, and the connective-based account. Finally we cover theories of local and global salience and its effects, including Gundel’s Activation Hierarchy theory and Grosz and Sidner’s theory of the local and global focus.

scholarly journals Regular semigroups, fundamental semigroups and groups

1980 ◽  
Vol 29 (4) ◽  
pp. 475-503 ◽  
Author(s):  
D. B. McAlister
Keyword(s):  
Regular Semigroup ◽  
Partial Order ◽  
Direct Product ◽  
Homomorphic Image ◽  
Sufficient Conditions ◽  
Main Tool ◽  
Natural Partial Order ◽  
Regular Semigroups ◽  
Necessary And Sufficient ◽  
Fundamental Semigroups

AbstractIn this paper we obtain necessary and sufficient conditions on a regular semigroup in order that it should be an idempotent separating homomorphic image of a full subsemigroup of the direct product of a group and a fundamental or combinatorial regular semigroup. The main tool used is the concept of a prehomomrphism θ: S → T between regular semigroups. This is a mapping such that (ab) θ ≦ aθ bθ in the natural partial order on T.

scholarly journals A STRONG OPERATOR TOPOLOGY ADIABATIC THEOREM

2002 ◽  
Vol 14 (06) ◽  
pp. 569-584 ◽  
Author(s):  
ALEXANDER ELGART ◽  
JEFFREY H. SCHENKER
Keyword(s):  
Spectral Data ◽  
Time Scale ◽  
Strong Operator Topology ◽  
Continuous Functions ◽  
Adiabatic Theorem ◽  
Strong Operator ◽  
Intrinsic Time ◽  
Embedded Eigenvalues ◽  
Additive Perturbation ◽  
Spectral Projections

We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in norm while for a larger class functions, including the spectral projections associated to embedded eigenvalues, the convergence is in the strong operator topology.

scholarly journals Enlargements of regular semigroups

1996 ◽  
Vol 39 (3) ◽  
pp. 425-460 ◽  
Author(s):  
M. V. Lawson
Keyword(s):  
Regular Semigroup ◽  
Semigroup Theory ◽  
Regular Semigroups

We introduce a class of regular extensions of regular semigroups, called enlargements; a regular semigroup T is said to be an enlargement of a regular subsemigroup S if S = STS and T = TST. We show that S and T have many properties in common, and that enlargements may be used to analyse a number of questions in regular semigroup theory.

scholarly journals A special sublattice of the congruence lattice of a regular semigroup

1997 ◽  
Vol 40 (3) ◽  
pp. 457-472 ◽  
Author(s):  
Mario Petrich
Keyword(s):  
Distributive Lattice ◽  
Regular Semigroup ◽  
Congruence Lattice ◽  
Regular Semigroups ◽  
Generators And Relations ◽  
Completely Regular ◽  
Completely Simple Semigroups ◽  
Special Cases ◽  
Completely Regular Semigroups ◽  
Completely Simple

Let S be a regular semigroup and be its congruence lattice. For ρ ∈ , we consider the sublattice Lρ of generated by the congruences pw where w ∈ {K, k, T, t}* and w has no subword of the form KT, TK, kt, tk. Here K, k, T, t are the operators on induced by the kernel and the trace relations on . We find explicitly the least lattice L whose homomorphic image is Lρ for all ρ ∈ and represent it as a distributive lattice in terms of generators and relations. We also consider special cases: bands of groups, E-unitary regular semigroups, completely simple semigroups, rectangular groups as well as varieties of completely regular semigroups.

REGULAR SEMIGROUPS WITH NORMAL IDEMPOTENTS

2017 ◽  
Vol 103 (1) ◽  
pp. 116-125
Author(s):  
XIANGFEI NI ◽  
HAIZHOU CHAO
Keyword(s):  
Regular Semigroup ◽  
Simple Method ◽  
Regular Semigroups

In this paper, we investigate regular semigroups that possess a normal idempotent. First, we construct a nonorthodox nonidempotent-generated regular semigroup which has a normal idempotent. Furthermore, normal idempotents are described in several different ways and their properties are discussed. These results enable us to provide conditions under which a regular semigroup having a normal idempotent must be orthodox. Finally, we obtain a simple method for constructing all regular semigroups that contain a normal idempotent.

Problem Solving: Help in the Right Direction for LD Students

1982 ◽  
Vol 29 (6) ◽  
pp. 26-41
Author(s):  
Carol A. Thornton ◽  
Nancy S. Bley
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Upper Elementary ◽  
Elementary Grades ◽  
Basic Facts ◽  
The Right

Until recently problem solving was stressed primarily in the middle and upper elementary grades. The focus in the lower grades was on memorizing basic facts and developing specific computational skills. When children reached the middle elementary grades it was often assumed that because they could compute they also would know when to apply the different operations in problem-solving contexts. Unfortunately this is not always the case. Problem solving involves more than incorporating computational skills. It primarily requires a great deal of decision making.

scholarly journals A NEW CONSTRUCTION FOR REGULAR SEMIGROUPS WITH QUASI-IDEAL ORTHODOX TRANSVERSALS

2009 ◽  
Vol 86 (2) ◽  
pp. 177-187 ◽  
Author(s):  
XIANGJUN KONG ◽  
XIANZHONG ZHAO
Keyword(s):  
Regular Semigroup ◽  
Structure Theorem ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Green’S Relations ◽  
Regular Semigroups ◽  
New Construction ◽  
Necessary And Sufficient ◽  
Equivalent Conditions ◽  
Orthodox Semigroups

AbstractIn any regular semigroup with an orthodox transversal, we define two sets R and L using Green’s relations and give necessary and sufficient conditions for them to be subsemigroups. By using R and L, some equivalent conditions for an orthodox transversal to be a quasi-ideal are obtained. Finally, we give a structure theorem for regular semigroups with quasi-ideal orthodox transversals by two orthodox semigroups R and L.

scholarly journals Idempotent-generated regular semigroups

1973 ◽  
Vol 15 (1) ◽  
pp. 27-34 ◽  
Author(s):  
C. Eberhart ◽  
W. Williams ◽  
L. Kinch
Keyword(s):  
Regular Semigroup ◽  
Regular Semigroups

Suppose S is a regular semigroup and E is its set of idempotents. If E is subsemigroup of S, then S has been called orthodox and studied recently by Hall [3], Meakin [6], and Yamada [8]. In this paper we assume that E is not (necessarily) a subsemigroup of S and consider the subsemigroup generated by E, denoted <E>. If E denotes the set of all elements of S which can be written E, denoted <E>. If E denotes the set of all elements of S which can be written as the product of n (not necessarily distinct) idempotents of S, then . We show that <E> is always a regular subsemigroup of S and investigate relationships between it and S. The case where <E> = S is of particular interest to us; such semigroups will be referred to as idempotent-generated regular semi- groups.

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