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Hardcover ISBN:  9780821803899 
Product Code:  SURV/42 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412739 
Product Code:  SURV/42.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821803899 
eBook ISBN:  9781470412739 
Product Code:  SURV/42.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 42; 1995; 293 ppMSC: Primary 06; Secondary 68
This book explores the surprisingly rich and complex structure of free lattices. The first part of the book presents a complete exposition of the basic theory of free lattices, projective lattices, and lattices which are bounded homomorphic images of a free lattice, as well as applications of these results to other areas. This portion of the book is suitable for use in a graduate course in lattice theory or general algebra. The second part of the book contains new results about free lattices and new proofs of known results, providing the reader with a coherent picture of the fine structure of free lattices. The book closes with an analysis of algorithms for free lattices and finite lattices that is accessible to researchers in other areas and depends only on the first chapter and a small part of the second. Several open problems appear throughout the book and, for easy reference, are assembled in a section at the end. Synthesizing seventy years of research, this is the only comprehensive treatment available of the theory of free lattices.
ReadershipMathematicians interested in algebra and lattice theory in particular. Mathematicians with an interest in algorithms in lattice theory and their complexities.

Table of Contents

Chapters

I. Whitman’s solution to the word problem

II. Bounded homomorphisms and related concepts

III. Covers in free lattices

IV. Day’s theorem revisited

V. Sublattices of free lattices and projective lattices

VI. Totally atomic elements

VII. Finite intervals and connected components

VIII. Singular and semisingular elements

IX. Tschantz’s theorem and maximal chains

X. Infinite intervals

XI. Computational aspects of lattice theory

XII. Term rewrite systems and varieties of lattices


Reviews

Researchers in lattice theory will find much of interest. The comprehensive nature of this book guarantees that those interested in further research in lattices will find this book indispensable.
An extensive body of results on free lattices exists, and the twelve chapters of this book provide a comprehensive yet engaging survey of these results ... Anyone working in lattice theory or in the study of free algebraic systems should certainly have access to a copy.
Bulletin of the AMS 
This scholarly text covers the fascinating subject of free lattices, the general structure of which is very complex. Beautifully set using TeX, and reasonably priced, it provides the lattice theorist with a wealth of information on the subject and is sure to become a classic reference. The reader can be assured of the quality of the exposition simply from the names of the author ... The book ends with a collection of 14 challenging open problems and a useful bibliography.
Mathematical Reviews 
Well written and has an abundance of wellchosen examples.
Zentralblatt MATH 
An extensive body of results on free lattices exists, and the twelve chapters of this book provide a comprehensive yet engaging survey of these results ... Anyone working in lattice theory or in the study of free algebraic systems should certainly have access to a copy.
Bulletin of the London Mathematical Society 
A beautiful book which collects all what is known on free lattices!
Monatshefte für Mathematik


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This book explores the surprisingly rich and complex structure of free lattices. The first part of the book presents a complete exposition of the basic theory of free lattices, projective lattices, and lattices which are bounded homomorphic images of a free lattice, as well as applications of these results to other areas. This portion of the book is suitable for use in a graduate course in lattice theory or general algebra. The second part of the book contains new results about free lattices and new proofs of known results, providing the reader with a coherent picture of the fine structure of free lattices. The book closes with an analysis of algorithms for free lattices and finite lattices that is accessible to researchers in other areas and depends only on the first chapter and a small part of the second. Several open problems appear throughout the book and, for easy reference, are assembled in a section at the end. Synthesizing seventy years of research, this is the only comprehensive treatment available of the theory of free lattices.
Mathematicians interested in algebra and lattice theory in particular. Mathematicians with an interest in algorithms in lattice theory and their complexities.

Chapters

I. Whitman’s solution to the word problem

II. Bounded homomorphisms and related concepts

III. Covers in free lattices

IV. Day’s theorem revisited

V. Sublattices of free lattices and projective lattices

VI. Totally atomic elements

VII. Finite intervals and connected components

VIII. Singular and semisingular elements

IX. Tschantz’s theorem and maximal chains

X. Infinite intervals

XI. Computational aspects of lattice theory

XII. Term rewrite systems and varieties of lattices

Researchers in lattice theory will find much of interest. The comprehensive nature of this book guarantees that those interested in further research in lattices will find this book indispensable.
An extensive body of results on free lattices exists, and the twelve chapters of this book provide a comprehensive yet engaging survey of these results ... Anyone working in lattice theory or in the study of free algebraic systems should certainly have access to a copy.
Bulletin of the AMS 
This scholarly text covers the fascinating subject of free lattices, the general structure of which is very complex. Beautifully set using TeX, and reasonably priced, it provides the lattice theorist with a wealth of information on the subject and is sure to become a classic reference. The reader can be assured of the quality of the exposition simply from the names of the author ... The book ends with a collection of 14 challenging open problems and a useful bibliography.
Mathematical Reviews 
Well written and has an abundance of wellchosen examples.
Zentralblatt MATH 
An extensive body of results on free lattices exists, and the twelve chapters of this book provide a comprehensive yet engaging survey of these results ... Anyone working in lattice theory or in the study of free algebraic systems should certainly have access to a copy.
Bulletin of the London Mathematical Society 
A beautiful book which collects all what is known on free lattices!
Monatshefte für Mathematik