Lattice theory : special topics and applications
Author(s)
Bibliographic Information
Lattice theory : special topics and applications
Birkhäuser , Springer, c2014-
- v. 1 : [pbk]
- v. 2 : [pbk]
Available at / 10 libraries
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Science and Technology Library, Kyushu University
v. 1 : [pbk]P 014/LATT/1-1033212014003826,
v. 2 : [pbk]P 016/LATT/1-2033212016005898 -
Kyoto Sangyo University Library
v. 1 : [pbk]411.74||GRA||101333136,
v. 2 : [pbk]411.74||GRA||201333137 -
Library, Research Institute for Mathematical Sciences, Kyoto University数研
v. 1 : [pbk]GRA||13||7-1200032306793
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Note
Bibliography: v. 1: p. 437-460 ; v. 2: p. 563-597
Description and Table of Contents
- Volume
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v. 1 : [pbk] ISBN 9783319064123
Description
George Gratzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Gratzer 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 Gratzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Gratzer.
Table of Contents
Introduction. Part I Topology and Lattices.- Chapter 1. Continuous and Completely Distributive Lattices.- Chapter 2. Frames: Topology Without Points.- Part II. Special Classes of Finite Lattices.- Chapter 3. Planar Semi modular Lattices: Structure and Diagram.- Chapter 4. Planar Semi modular Lattices: Congruences.- Chapter 5. Sectionally Complemented Lattices.- Chapter 6. Combinatorics in finite lattices.- Part III. Congruence Lattices of Infinite Lattices and Beyond.- Chapter 7. Schmidt and Pudlak's Approaches to CLP.- Chapter 8. Congruences of lattices and ideals of rings.- Chapter 9. Liftable and Unliftable Diagrams.- Chapter 10. Two topics related to congruence lattices of lattices.
- Volume
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v. 2 : [pbk] ISBN 9783319442358
Description
George Gratzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Gratzer 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, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation.
This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
Table of Contents
Varieties of Lattices.- Free and Finitely Presented Lattices.- Classes of Semidistributive Lattices.- Lattices of Algebraic Subsets and Implicational Classes.- Convex Geometries.- Bases of Closure Systems.- Permutohedra and Associahedra.- Generalizations of the Permutohedron.- Lattice Theory of the Poset of Regions.- Finite Coxeter Groups and the Weak Order.
by "Nielsen BookData"
