Nonmodular Lattice Varieties PDF Download
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Author: Henry Rose
Publisher: American Mathematical Soc.
ISBN: 0821822926
Category : Mathematics
Languages : en
Pages : 85
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Book Description
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.
Author: Henry Rose
Publisher: American Mathematical Soc.
ISBN: 0821822926
Category : Mathematics
Languages : en
Pages : 85
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Book Description
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.
Author: Peter Jipsen
Publisher: Springer
ISBN: 3540475141
Category : Mathematics
Languages : en
Pages : 171
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Book Description
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: Manfred Stern
Publisher: Cambridge University Press
ISBN: 0521461057
Category : Mathematics
Languages : en
Pages : 386
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Book Description
A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.
Author: Ralph S. Freese
Publisher: American Mathematical Society
ISBN: 1470467976
Category : Mathematics
Languages : en
Pages : 496
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Book Description
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: Jennifer Hyndman
Publisher: Springer
ISBN: 3319782355
Category : Computers
Languages : en
Pages : 173
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Book Description
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:
Publisher: American Mathematical Soc.
ISBN: 9780821895887
Category : Mathematics
Languages : en
Pages : 262
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Book Description
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.
Author: L.N. Shevrin
Publisher: Springer Science & Business Media
ISBN: 9401587515
Category : Mathematics
Languages : en
Pages : 389
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Book Description
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.
Author: Ralph S. Freese
Publisher: American Mathematical Soc.
ISBN: 0821803891
Category : Mathematics
Languages : en
Pages : 304
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Book Description
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: Bogart
Publisher: Springer Science & Business Media
ISBN: 1489935584
Category : Science
Languages : en
Pages : 476
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Book Description
Author: Kira Adaricheva
Publisher: Springer Nature
ISBN: 303098088X
Category : Mathematics
Languages : en
Pages : 293
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Book Description
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.
