## Introduction to lattices and order / B. A. Davey, H. A. Priestley.

Editor: Cambridge : Cambridge University Press, 1990Descripción: viii, 248 p. : il. ; 23 cmISBN: 0521367662 (pbk.); 0521365848Tema(s): Lattice theoryOtra clasificación: 06-01 (68Q55) Recursos en línea: Publisher descriptionPreface vii 1. Ordered sets [1] Ordered sets [1] Examples from mathematics, computer science and social science [3] Diagrams [7] Maps between ordered sets [10] The Duality Principle; down-sets and up-sets [12] Maximal and minimal elements; top and bottom [15] Building new ordered sets [17] Exercises [21] 2. Lattices and complete lattices [27] Lattices as ordered sets [27] Complete lattices [33] Chain conditions and completeness [37] Completions [40] Exercises [45] 3. CPOs, algebraic lattices and domains [50] Directed joins and algebraic closure operators [51] CPOs [54] Finiteness, algebraic lattices and domains [58] Information systems [63] Exercises [79] 4. Fixpoint theorems [86] Fixpoint theorems and their applications [86] The existence of maximal elements and Zorn’s Lemma [99] Exercises [103] 5. Lattices as algebraic structures [109] Lattices as algebraic structures [109] Sublattices, products and homomorphisms [111] Congruences [114] Exercises [123] 6. Modular and distributive lattices [130] Lattices satisfying additional identities [130] The M3-N5 Theorem [134] Exercises [133] 7. Boolean algebras and their applications [143] Boolean algebras [143] Boolean terms and disjunctive normal form [146] Meet LINDA: the Lindenbaum algebra [154] Exercises [158] 8. Representation theory: the finite case [163] The representation of finite Boolean algebras [163] Join-irreducible elements [165] The representation of finite distributive lattices [169] Duality between finite distributive lattices and finite ordered sets [171] Exercises [177] 9. Ideals and filters [184] Ideals and filters [184] Prime ideals, maximal ideals and ultrafilters [185] The existence of prime ideals, maximal ideals and ultrafilters [187] Exercises [190] 10. Representation theory: the general case [193] Representation by lattices of sets [193] The prime ideal space [195] Duality [201] Appendix: a topological toolkit [210] Exercises [214] 11. Formal concept analysis [221] Contexts and their concepts [221] The fundamental theorem [223] From theory to practice [227] Exercises [231] Appendix: further reading [237] Notation index [241] Index [243]

Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|

Libros | Instituto de Matemática, CONICET-UNS | 06 D248 (Browse shelf) | Available | A-6493 |

Bibliografía: p. [237]-240.

Preface vii --

1. Ordered sets [1] --

Ordered sets [1] --

Examples from mathematics, computer science and social science [3] --

Diagrams [7] --

Maps between ordered sets [10] --

The Duality Principle; down-sets and up-sets [12] --

Maximal and minimal elements; top and bottom [15] --

Building new ordered sets [17] --

Exercises [21] --

2. Lattices and complete lattices [27] --

Lattices as ordered sets [27] --

Complete lattices [33] --

Chain conditions and completeness [37] --

Completions [40] --

Exercises [45] --

3. CPOs, algebraic lattices and domains [50] --

Directed joins and algebraic closure operators [51] --

CPOs [54] --

Finiteness, algebraic lattices and domains [58] --

Information systems [63] --

Exercises [79] --

4. Fixpoint theorems [86] --

Fixpoint theorems and their applications [86] --

The existence of maximal elements and Zorn’s Lemma [99] --

Exercises [103] --

5. Lattices as algebraic structures [109] --

Lattices as algebraic structures [109] --

Sublattices, products and homomorphisms [111] --

Congruences [114] --

Exercises [123] --

6. Modular and distributive lattices [130] --

Lattices satisfying additional identities [130] --

The M3-N5 Theorem [134] --

Exercises [133] --

7. Boolean algebras and their applications [143] --

Boolean algebras [143] --

Boolean terms and disjunctive normal form [146] --

Meet LINDA: the Lindenbaum algebra [154] --

Exercises [158] --

8. Representation theory: the finite case [163] --

The representation of finite Boolean algebras [163] --

Join-irreducible elements [165] --

The representation of finite distributive lattices [169] --

Duality between finite distributive lattices and finite ordered sets [171] --

Exercises [177] --

9. Ideals and filters [184] --

Ideals and filters [184] --

Prime ideals, maximal ideals and ultrafilters [185] --

The existence of prime ideals, maximal ideals and ultrafilters [187] --

Exercises [190] --

10. Representation theory: the general case [193] --

Representation by lattices of sets [193] --

The prime ideal space [195] --

Duality [201] --

Appendix: a topological toolkit [210] --

Exercises [214] --

11. Formal concept analysis [221] --

Contexts and their concepts [221] --

The fundamental theorem [223] --

From theory to practice [227] --

Exercises [231] --

Appendix: further reading [237] --

Notation index [241] --

Index [243] --

MR, 91h:06001

There are no comments on this title.