A Primer Of Subquasivariety Lattices
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| Author | : Kira Adaricheva |
| Publisher | : Springer Nature |
| Total Pages | : 293 |
| Release | : 2022-08-18 |
| Genre | : Mathematics |
| ISBN | : 303098088X |
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator. As an application of this new approach, it is shown that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book contains many examples to illustrate these principles, as well as open problems. Ultimately this new approach gives readers a set of tools to investigate classes of lattices that can be represented as subquasivariety lattices.
| Author | : Kira Adaricheva |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : Electronic books |
| ISBN | : 9788303098085 |
This book addresses Birkhoff and Mal'cev's problem of describing subquasivariety lattices. The text begins by developing the basics of atomic theories and implicational theories in languages that may, or may not, contain equality. Subquasivariety lattices are represented as lattices of closed algebraic subsets of a lattice with operators, which yields new restrictions on the equaclosure operator. As an application of this new approach, it is shown that completely distributive lattices with a dually compact least element are subquasivariety lattices. The book contains many examples to illustrate these principles, as well as open problems. Ultimately this new approach gives readers a set of tools to investigate classes of lattices that can be represented as subquasivariety lattices.
| Author | : Jennifer Hyndman |
| Publisher | : Springer |
| Total Pages | : 173 |
| Release | : 2018-08-28 |
| Genre | : Computers |
| ISBN | : 3319782355 |
This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.
| Author | : Ralph S. Freese |
| Publisher | : American Mathematical Society |
| Total Pages | : 496 |
| Release | : 2022-10-28 |
| Genre | : Mathematics |
| ISBN | : 1470467976 |
This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.
| Author | : Greg Gibson |
| Publisher | : Sinauer |
| Total Pages | : 0 |
| Release | : 2009-04-20 |
| Genre | : Science |
| ISBN | : 9780878932368 |
An accessible introduction to the field of genome science, it explains bioinformatic principles and experimental strategies alongside experimental methods. This edition has been updated to include the latest developments in next generation sequencing, high-volume genotyping and expression profiling, and advances in metabolomics.
| Author | : George Grätzer |
| Publisher | : Springer |
| Total Pages | : 472 |
| Release | : 2014-08-27 |
| Genre | : Mathematics |
| ISBN | : 3319064134 |
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.
| Author | : Ralph S. Freese |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 304 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821803891 |
A thorough treatment of free lattices, including such aspects as Whitman's solution to the word problem, bounded monomorphisms and related concepts, totally atomic elements, infinite intervals, computation, term rewrite systems, and varieties. Includes several results that are new or have not been previously published. Annotation copyright by Book News, Inc., Portland, OR
| Author | : Peter Jipsen |
| Publisher | : Springer |
| Total Pages | : 171 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540475141 |
The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.
| Author | : Fabrizio Frezza |
| Publisher | : Springer |
| Total Pages | : 177 |
| Release | : 2015-04-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3319165747 |
This book is a concise introduction to electromagnetics and electromagnetic fields that covers the aspects of most significance for engineering applications by means of a rigorous, analytical treatment. After an introduction to equations and basic theorems, topics of fundamental theoretical and applicative importance, including plane waves, transmission lines, waveguides and Green's functions, are discussed in a deliberately general way. Care has been taken to ensure that the text is readily accessible and self-consistent, with conservation of the intermediate steps in the analytical derivations. The book offers the reader a clear, succinct course in basic electromagnetic theory. It will also be a useful lookup tool for students and designers.
| Author | : James Nation |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 310 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401000646 |
A cutting-edge survey of formal methods directed specifically at dealing with the deep mathematical problems engendered by the study of developing systems, in particular dealing with developing phase spaces, changing components, structures and functionalities, and the problem of emergence. Several papers deal with the modelling of particular experimental situations in population biology, economics and plant and muscle developments in addition to purely theoretical approaches. Novel approaches include differential inclusions and viability theory, growth tensors, archetypal dynamics, ensembles with variable structures, and complex system models. The papers represent the work of theoreticians and experimental biologists, psychologists and economists. The areas covered embrace complex systems, the development of artificial life, mathematics, computer science, biology and psychology.
