Ralph S. Freese's Books

Algebras, Lattices, Varieties

Volume II

By: Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor

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Algebras, Lattices, Varieties

Volume II

By: Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor

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.

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Page Count

496

Publisher

American Mathematical Society

Published Date

ISBN 10

1470467976

ISBN 13

9781470467975

Free Lattices

By: Ralph S. Freese,Jaroslav Ježek,James Bryant Nation

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Free Lattices

By: Ralph S. Freese,Jaroslav Ježek,James Bryant Nation

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

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304

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803891

ISBN 13

9780821803899

The Structure of Modular Lattices of Width Four with Applications to Varieties of Lattices

By: Ralph S. Freese

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The Structure of Modular Lattices of Width Four with Applications to Varieties of Lattices

By: Ralph S. Freese

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.

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Page Count

103

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821821814

ISBN 13

9780821821817

Book's by Ralph S. Freese

Algebras, Lattices, Varieties

Algebras, Lattices, Varieties

Free Lattices

Free Lattices

The Structure of Modular Lattices of Width Four with Applications to Varieties of Lattices

The Structure of Modular Lattices of Width Four with Applications to Varieties of Lattices

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