Download or read book Nonmodular Lattice Varieties written by Henry Rose and published by American Mathematical Soc.. This book was released on 1984 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that there are eight infinite sequences of join irreducible lattice varieties with the following properties: each term of every sequence has the next term as its unique join irreducible cover. The description of these sequences is based on a detailed study of subdirectly irreducible lattices with the unique critical quotients.
Download or read book Varieties of Lattices written by Peter Jipsen and published by Springer. This book was released on 2006-11-15 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lattice Varieties Covering the Smallest Non modular Variety written by Bjarni Jónsson and published by . This book was released on 1976 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Lattice of Interpretability Types of Varieties written by Octavio Carlos García and published by American Mathematical Soc.. This book was released on 1984 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: We investigate the lattice, invented by W. D. Neumann in 1974, formed by the class of all varieties under the quasi-ordering "[script]V is interpretable in [script]W." The lattice is found to be non-modular and a proper class. Various familiar varieties are found to be [logical conjunction symbol {up arrow}]-irreducible (or prime) and various filters (especially Mal'tsev classes) are found to be indecomposable (or prime). Many familiar varieties are found to be inequivalent in the lattice, using a new technique of SIN algebras. Seven figures are included which document the known relationships between some sixty known or easily describable varieties and varietal families.
Download or read book The Structure of Modular Lattices of Width Four with Applications to Varieties of Lattices written by Ralph S. Freese and published by American Mathematical Soc.. This book was released on 1977 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: A variety (equational class) of lattices is said to be finitely based if there exists a finite set of identities defining the variety. Let [capital script]M [infinity symbol] [over][subscript italic]n denote the lattice variety generated by all modular lattices of width not exceeding [subscript italic]n. [capital script]M [infinity symbol] [over]1 and [capital script]M [infinity symbol] [over]2 are both the class of all distributive lattices and consequently finitely based. B. Jónsson has shown that [capital script]M [infinity symbol] [over]3 is also finitely based. On the other hand, K. Baker has shown that [capital script]M [infinity symbol] [over][subscript italic]n is not finitely based for 5 [less than or equal to symbol] [italic]n [less than] [lowercase Greek]Omega. This paper settles the finite bases problem for [capital script]M [infinity symbol] [over]4.
Download or read book P a Nontrivial Modular Lattice Variety and V a Nonmodular Lattice Variety Such that VoP is a Variety Implies V is the Variety of All Lattices written by Thomas Arthur Harrison and published by . This book was released on 1985 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Algebras Lattices Varieties written by Ralph S. Freese and published by American Mathematical Society. This book was released on 2022-11-03 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third 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.
Download or read book Algebras Lattices Varieties written by Ralph N. McKenzie and published by American Mathematical Society. This book was released on 2018-07-09 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.
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.
Download or read book Varieties of Lattices written by Peter Jipsen and published by . This book was released on 2014-01-15 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Structure of Modular Lattices of Width Four with Applications to Varieties of Lattices written by Ralph S. Freese and published by American Mathematical Soc.. This book was released on 1977-12-31 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordered Sets and Lattices II written by and published by American Mathematical Soc.. This book was released on with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
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.
Download or read book The Dilworth Theorems written by Bogart and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Free Lattices written by Ralph S. Freese and published by American Mathematical Soc.. This book was released on 1995 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Lattice of Subquasivarieties of a Locally Finite Quasivariety written by Jennifer Hyndman and published by Springer. This book was released on 2018-08-28 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Primer of Subquasivariety Lattices written by Kira Adaricheva and published by Springer Nature. This book was released on 2022-08-18 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
