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Semigroups In Complete Lattices
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Book Synopsis Semigroups in Complete Lattices by : Patrik Eklund
Download or read book Semigroups in Complete Lattices written by Patrik Eklund and published by Springer. This book was released on 2018-06-09 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research. This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.
Book Synopsis Semigroups and Their Subsemigroup Lattices by : L.N. Shevrin
Download or read book Semigroups and Their Subsemigroup Lattices written by L.N. Shevrin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A partially ordered by inclusion forms a lattice. This is the subsystem lattice of A. (In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years. This trend was formed first in group theory; basic relevant information up to the early seventies is contained in the book [Suz] and the surveys [K Pek St], [Sad 2], [Ar Sad], there is also a quite recent book [Schm 2]. As another inspiring source, one should point out a branch of mathematics to which the book [Baer] was devoted. One of the key objects of examination in this branch is the subspace lattice of a vector space over a skew field. A more general approach deals with modules and their submodule lattices. Examining subsystem lattices for the case of modules as well as for rings and algebras (both associative and non-associative, in particular, Lie algebras) began more than thirty years ago; there are results on this subject also for lattices, Boolean algebras and some other types of algebraic systems, both concrete and general. A lot of works including several surveys have been published here.
Book Synopsis The Algebraic Theory of Semigroups, Volume II by : Alfred Hoblitzelle Clifford
Download or read book The Algebraic Theory of Semigroups, Volume II written by Alfred Hoblitzelle Clifford and published by American Mathematical Soc.. This book was released on 1961 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homological Algebra by : Marco Grandis
Download or read book Homological Algebra written by Marco Grandis and published by World Scientific. This book was released on 2012 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations. These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system. The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a 'Coherence Theorem for homological algebra'. (On the contrary, a 'non-distributive' homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.) The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences. We thus establish an effective method of working with spectral sequences, called 'crossword chasing', that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.
Book Synopsis Lattices and Ordered Algebraic Structures by : T.S. Blyth
Download or read book Lattices and Ordered Algebraic Structures written by T.S. Blyth and published by Springer Science & Business Media. This book was released on 2005-04-18 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS
Book Synopsis M-Solid Varieties of Algebras by : Jörg Koppitz
Download or read book M-Solid Varieties of Algebras written by Jörg Koppitz and published by Springer Science & Business Media. This book was released on 2006-02-10 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: A complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on solid varieties of semirings and semigroups. The book aims to develop the theory of solid varieties as a system of mathematical discourse that is applicable in several concrete situations. A unique feature of this book is the use of Galois connections to integrate different topics.
Book Synopsis Lattices, Semigroups, and Universal Algebra by : Jorge Almeida
Download or read book Lattices, Semigroups, and Universal Algebra written by Jorge Almeida and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis One-parameter Semigroups of Positive Operators by : Wolfgang Arendt
Download or read book One-parameter Semigroups of Positive Operators written by Wolfgang Arendt and published by Springer. This book was released on 2006-11-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Semirings: Algebraic Theory And Applications In Computer Science by : Hanns Joachim Weinert
Download or read book Semirings: Algebraic Theory And Applications In Computer Science written by Hanns Joachim Weinert and published by World Scientific. This book was released on 1998-10-30 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the algebraic theory of semirings and, in this context, to basic algebraic concepts as e.g. semigroups, lattices and rings. It includes an algebraic theory of infinite sums as well as a detailed treatment of several applications in theoretical computer science. Complete proofs, various examples and exercises (some of them with solutions) make the book suitable for self-study. On the other hand, a more experienced reader who looks for information about the most common concepts and results on semirings will find cross-references throughout the book, a comprehensive bibliography and various hints to it.
Book Synopsis Introduction to Lattice Theory with Computer Science Applications by : Vijay K. Garg
Download or read book Introduction to Lattice Theory with Computer Science Applications written by Vijay K. Garg and published by John Wiley & Sons. This book was released on 2016-03-02 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author’s intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory Provides end of chapter exercises to help readers retain newfound knowledge on each subject Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.
Book Synopsis Residuated Lattices: An Algebraic Glimpse at Substructural Logics by : Nikolaos Galatos
Download or read book Residuated Lattices: An Algebraic Glimpse at Substructural Logics written by Nikolaos Galatos and published by Elsevier. This book was released on 2007-04-25 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.
Book Synopsis Semigroups and Their Applications by : Simon M. Goberstein
Download or read book Semigroups and Their Applications written by Simon M. Goberstein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Positive Operators and Semigroups on Banach Lattices by : C.B. Huijsmans
Download or read book Positive Operators and Semigroups on Banach Lattices written by C.B. Huijsmans and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last twenty-five years, the development of the theory of Banach lattices has stimulated new directions of research in the theory of positive operators and the theory of semigroups of positive operators. In particular, the recent investigations in the structure of the lattice ordered (Banach) algebra of the order bounded operators of a Banach lattice have led to many important results in the spectral theory of positive operators. The contributions contained in this volume were presented as lectures at a conference organized by the Caribbean Mathematics Foundation, and provide an overview of the present state of development of various areas of the theory of positive operators and their spectral properties. This book will be of interest to analysts whose work involves positive matrices and positive operators.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1994-03 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Concise Handbook of Algebra by : Alexander V. Mikhalev
Download or read book The Concise Handbook of Algebra written by Alexander V. Mikhalev and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is by no means clear what comprises the "heart" or "core" of algebra, the part of algebra which every algebraist should know. Hence we feel that a book on "our heart" might be useful. We have tried to catch this heart in a collection of about 150 short sections, written by leading algebraists in these areas. These sections are organized in 9 chapters A, B, . . . , I. Of course, the selection is partly based on personal preferences, and we ask you for your understanding if some selections do not meet your taste (for unknown reasons, we only had problems in the chapter "Groups" to get enough articles in time). We hope that this book sets up a standard of what all algebraists are supposed to know in "their" chapters; interested people from other areas should be able to get a quick idea about the area. So the target group consists of anyone interested in algebra, from graduate students to established researchers, including those who want to obtain a quick overview or a better understanding of our selected topics. The prerequisites are something like the contents of standard textbooks on higher algebra. This book should also enable the reader to read the "big" Handbook (Hazewinkel 1999-) and other handbooks. In case of multiple authors, the authors are listed alphabetically; so their order has nothing to do with the amounts of their contributions.
Book Synopsis The q-theory of Finite Semigroups by : John Rhodes
Download or read book The q-theory of Finite Semigroups written by John Rhodes and published by Springer Science & Business Media. This book was released on 2009-04-05 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive, encyclopedic text in four parts aims to give the reader — from the graduate student to the researcher/practitioner — a detailed understanding of modern finite semigroup theory, focusing in particular on advanced topics on the cutting edge of research. The q-theory of Finite Semigroups presents important techniques and results, many for the first time in book form, thereby updating and modernizing the semigroup theory literature.
Book Synopsis Semimodular Lattices by : Manfred Stern
Download or read book Semimodular Lattices written by Manfred Stern and published by Cambridge University Press. This book was released on 1999-05-13 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.
