Completely Regular Semigroup Varieties
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Completely Regular Semigroup Varieties
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Author : Mario Petrich
language : en
Publisher: Springer Nature
Release Date : 2025-02-04
Completely Regular Semigroup Varieties written by Mario Petrich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-04 with Mathematics categories.
This book presents further developments and applications in the area of completely regular semigroup theory, beginning with applications of Polák’s theorem to obtain detailed descriptions of various kernel classes including the K-class covers of the kernel class of all bands. The important property of modularity of the lattice of varieties of completely regular semigroups is then employed to analyse various principal sublattices. This is followed by a study of certain important complete congruences on the lattice; the group, local and core relations. The next chapter is devoted to a further treatment of certain free objects and related word problems. There are many constructions in the theory of semigroups. Those that have played an important role in the theory of varieties of completely regular semigroups are presented as they apply in this context. The mapping that takes each variety to its intersection with the variety of bands is a complete retraction of the lattice of varieties of completely regular semigroups onto the lattice of band varieties and so induces a complete congruence for which every class has a greatest member. The sublattice generated by these greatest members is then investigated with the help of many applications of Polák’s theorem. The book closes with a fascinating conjecture regarding the structure of this sublattice.
Completely Regular Semigroup Varieties
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Author : Mario Petrich
language : en
Publisher: Springer Nature
Release Date : 2024-03-11
Completely Regular Semigroup Varieties written by Mario Petrich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-11 with Mathematics categories.
This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today. This volume focuses on the lattice of varieties of completely regular semigroups. Since any in-depth study of the lattice of varieties requires an understanding of free completely regular semigroups, the book begins by describing the free object on countably infinite sets and the properties of the lattice of fully invariant congruences on the free object. The authors introduce various associated relations and operators on the lattice of varieties of completely regular semigroups. Following that, the book covers the sublattice of varieties of bands with a focus on the influence of that sublattice on the structure of the whole lattice. The book concludes with the remarkable theorem due to Polák describing the whole lattice of varieties of completely regular as a subdirect product of lattices,some of which are well understood. The authors include recent advances, insights, results, and techniques throughout the book.
Semigroups And Their Applications
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Author : Simon M. Goberstein
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Semigroups And Their Applications written by Simon M. Goberstein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Most papers published in this volume are based on lectures presented at the Chico Conference on Semigroups held on the Chico campus of the Cal ifornia State University on April 10-12, 1986. The conference was spon sored by the California State University, Chico in cooperation with the Engineering Computer Sciences Department of the Pacific Gas and Electric Company. The program included seven 50-minute addresses and seventeen 30-minute lectures. Speakers were invited by the organizing committee consisting of S. M. Goberstein and P. M. Higgins. The purpose of the conference was to bring together some of the leading researchers in the area of semigroup theory for a discussion of major recent developments in the field. The algebraic theory of semigroups is growing so rapidly and new important results are being produced at such a rate that the need for another meeting was well justified. It was hoped that the conference would help to disseminate new results more rapidly among those working in semi groups and related areas and that the exchange of ideas would stimulate research in the subject even further. These hopes were realized beyond all expectations.
Monoids And Semigroups With Applications Proceedings Of The Berkeley Workshop In Monoids
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Author : John Rhodes
language : en
Publisher: #N/A
Release Date : 1991-03-06
Monoids And Semigroups With Applications Proceedings Of The Berkeley Workshop In Monoids written by John Rhodes and has been published by #N/A this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-03-06 with categories.
The purpose of the Berkeley Workshop on Monoids was to give expository talks by the most qualified experts in the emerging main areas of monoid and semigroup theory including applications to theoretical computer science. This was supplemented with current research papers. The topics covered, in an accessible way for the mathematical and theoretical computer community, were: Kernels and expansions in semigroup theory; Implicit operations; Inverse monoids; Varieties of semigroups and universal algebra; Linear semigroups and monoids of Lie type; Monoids acting on tress; Synthesis theorem, regular semigroups, and applications; Type-II conjecture; Application to theoretical computer science and decision problems.
Semigroups
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Author : T. E. Hall
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Semigroups written by T. E. Hall and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Semigroups is a collection of papers dealing with models of classical statistics, sequential computing machine, inverse semi-groups. One paper explains the structure of inverse semigroups that leads to P-semigroups or E-unitary inverse semigroups by utilizing the P-theorem of W.D. Nunn. Other papers explain the characterization of divisibility in the category of sets in terms of images and relations, as well as the universal aspects of completely simple semigroups, including amalgamation, the lattice of varieties, and the Hopf property. Another paper explains finite semigroups which are extensions of congruence-free semigroups, where their set of congruences forms a chain. The paper then shows how to construct such semigroups. A finite semigroup (which is decomposable into a direct product of cyclic semigroups which are not groups) is actually uniquely decomposable. One paper points out when a finite semigroup has such a decomposition, and how its non-group cyclic direct factors, if any, can be found. The collection can prove useful for mathematicians, statisticians, students, and professors of higher mathematics or computer science.
Words Languages And Combinatorics Ii Proceedings Of The International Conference
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Author : Masami Ito
language : en
Publisher: World Scientific
Release Date : 1994-09-19
Words Languages And Combinatorics Ii Proceedings Of The International Conference written by Masami Ito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-19 with categories.
The research results published in this set of proceedings range from pure semigroup theory to theoretical computer science, in particular formal languages and automata. Contributed by internationally recognized researchers, the papers address issues in the algebraic and combinatorial theories of semigroups, the structure theory of automata, the classification theory of formal languages and codes and applications of these theories to various areas like circuit testing, coding theory, or cryptography. The underlying theme is the semigroup and automaton theories and their role in certain applications.
Semigroup Theory Proceedings Of The Monash Conference On Semigroup Theory In Honor Of G B Preston
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Author : T E Hall
language : en
Publisher: World Scientific
Release Date : 1991-05-21
Semigroup Theory Proceedings Of The Monash Conference On Semigroup Theory In Honor Of G B Preston written by T E Hall and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-05-21 with categories.
This conference celebrated the 65th birthday of Professor G B Preston of Monash University. Containing contributions from almost all his mathematical progeny, the proceedings is a tribute to his influence on semigroup and Australian mathematics.
Semigroups Automata And Languages
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Author : Jorge Almeida
language : en
Publisher: World Scientific
Release Date : 1996-01-27
Semigroups Automata And Languages written by Jorge Almeida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-27 with categories.
The conference was a rare occasion for different schools and perspectives to meet in a single event, bringing together researchers interested in semigroups, automata and languages. The proceedings contain both surveys and research reports, which have been carefully refereed. They should be of value to both mathematicians and computer scientists.
Semigroups Algorithms Automata And Languages
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Author : Gracinda M. S. Gomes
language : en
Publisher: World Scientific
Release Date : 2002
Semigroups Algorithms Automata And Languages written by Gracinda M. S. Gomes and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
The thematic term on OC Semigroups, Algorithms, Automata and LanguagesOCO organized at the International Centre of Mathematics (Coimbra, Portugal) in MayOCoJuly 2001 was the gathering point for researchers working in the field of semigroups, algorithms, automata and languages. These areas were selected considering their huge recent developments, their potential applications, and the motivation from other fields of mathematics and computer science. This proceedings volume is a unique collection of advanced courses and original contributions on semigroups and their connections with logic, automata, languages, group theory, discrete dynamics, topology and complexity. A selection of open problems discussed during the thematic term is also included. Contents: Finite Semigroups: An Introduction to a Unified Theory of Pseudovarieties (J Almeida); On Existence Varieties of Regular Semigroups (K Auinger); Varieties of Languages (M J J Branco); A Short Introduction to Automatic Group Theory (C Choffrut); Some Results on Semigroup-Graded Rings (W D Munn); Profinite Groups and Applications to Finite Semigroups (L Ribes); Dynamics of Finite Semigroups (J Almeida); Finite Semigroups Imposing Tractable Constraints (A Bulatov et al.); On the Efficiency and Deficiency of Rees Matrix Semigroups (C M Campbell et al.); Some Pseudovariety Joins Involving Groups and Locally Trivial Semigroups (J C Costa); Partial Action of Groups on Relational Structures: A Connection Between Model Theory and Profinite Topology (T Coulbois); Some Relatives of Automatic and Hyperbolic Groups (M Hoffmann et al.); A Sampler of a Topological Approach to Inverse Semigroups (B Steinberg); Finite Semigroups and the Logical Description of Regular Languages (H Straubing); Diamonds are Forever: The Variety DA (P Tesson & D Th(r)rien); Decidability Problems in Finite Semigroups (P G Trotter); and other papers. Readership: Researchers, academics and graduate students in pure mathematics and computer science."
Lattices Semigroups And Universal Algebra
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Author : Jorge Almeida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lattices Semigroups And Universal Algebra written by Jorge Almeida and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.