Free lattices:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
1995
|
| Schriftenreihe: | Mathematical surveys and monographs
42 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 293 S. |
| ISBN: | 0821803891 |
Internformat
MARC
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| 100 | 1 | |a Freese, Ralph S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Free lattices |c Ralph Freese ; Jaroslav Ježek ; J. B. Nation |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1995 | |
| 300 | |a VIII, 293 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical surveys and monographs |v 42 | |
| 650 | 0 | 7 | |a Gittertheorie |0 (DE-588)4157394-8 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Ježek, Jaroslav |e Verfasser |4 aut | |
| 700 | 1 | |a Nation, J. B. |d 1948- |e Verfasser |0 (DE-588)1172035334 |4 aut | |
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| 830 | 0 | |a Mathematical surveys and monographs |v 42 |w (DE-604)BV000018014 |9 42 | |
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Datensatz im Suchindex
| _version_ | 1804124723808829440 |
|---|---|
| adam_text | Contents
Introduction 1
Chapter I. Whitman s Solution to the Word Problem 7
1. Basic Concepts from Lattice Theory 7
2. Free Lattices 10
3. Canonical Form 15
4. Continuity 19
5. Fixed Point Free Polynomials and Incompleteness 20
6. Sublattices of Free Lattices 22
Chapter II. Bounded Homomorphisms and Related Concepts 27
1. Bounded Homomorphisms 27
2. Continuity 37
3. Doubling and Congruences on a Finite Lattice 38
4. A Refinement of the D Relation 45
5. Semidistributive Lattices 49
6. Splitting Lattices 55
7. Day s Theorem: Free Lattices are Weakly Atomic 62
8. Applications to Congruence Varieties 65
Chapter III. Covers in Free Lattices 67
1. Elementary Theorems on Covers in Fh(X) 67
2. J closed Sets and the Standard Epimorphism 71
3. Finite Lower Bounded Lattices 74
4. The Lattice Lv(w) 76
5. Syntactic Algorithms 79
6. Examples 83
7. Connected Components and the Bottom of FL(X) 87
Chapter IV. Day s Theorem Revisited 91
Chapter V. Sublattices of Free Lattices and Projective Lattices 95
1. Projective Lattices 95
2. The Free Lattice Generated by an Ordered Set 104
3. Finite Sublattices of Free Lattices 108
4. Related Topics 126
5. Finite Subdirectly Irreducible Sublattices of Free Lattices 129
6. Summary 132
vii
viii CONTENTS
Chapter VI. Totally Atomic Elements 135
1. Characterization 135
2. Canonical Form of Kappa of a Totally Atomic Element 141
3. The Role of Totally Atomic Elements 145
Chapter VII. Finite Intervals and Connected Components 151
1. Chains of Covers 151
2. Finite Intervals 154
3. Three Element Intervals 157
4. Connected Components 160
Chapter VIII. Singular and Semisingular Elements 171
1. Semisingular Elements 171
2. Singular Elements 176
Chapter IX. Tschantz s Theorem and Maximal Chains 179
1. Tschantz s Theorem 179
2. Coverless Elements 184
3. Maximal Chains 185
Chapter X. Infinite Intervals 189
1. Tschantz Triples 189
2. Join Irreducible Elements that are not Canonical Joinands 198
3. Splittings of a Free Lattice 200
Chapter XL Computational Aspects of Lattice Theory 205
1. Preliminaries 205
2. Ordered Sets 208
3. Finite Lattices 215
4. Representations and Contexts 220
5. Congruence Lattices of Finite Lattices 221
6. Bounded Homomorphisms and Splitting Lattices 229
7. Antichains and Chain Partitions of Ordered Sets 235
8. Algorithms for Free Lattices 241
9. Finitely Presented Lattices 249
10. Diagrams 251
Chapter XII. Term Rewrite Systems and Varieties of Lattices 255
1. Term Rewrite Systems 256
2. No AC TRS for Lattice Theory 258
3. An Extension 261
4. The Variety Generated by Lv(w) 262
5. A Lattice Variety with AC TRS 268
6. More Varieties with AC TRS 274
Open Problems 279
Bibliography 281
List of Symbols 287
Index 289
|
| any_adam_object | 1 |
| author | Freese, Ralph S. Ježek, Jaroslav Nation, J. B. 1948- |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010304944 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:50:12Z |
| institution | BVB |
| isbn | 0821803891 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006856934 |
| oclc_num | 246873283 |
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| owner | DE-12 DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-188 |
| physical | VIII, 293 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Freese, Ralph S. Verfasser aut Free lattices Ralph Freese ; Jaroslav Ježek ; J. B. Nation Providence, RI American Math. Soc. 1995 VIII, 293 S. txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 42 Gittertheorie (DE-588)4157394-8 gnd rswk-swf Gittertheorie (DE-588)4157394-8 s DE-604 Ježek, Jaroslav Verfasser aut Nation, J. B. 1948- Verfasser (DE-588)1172035334 aut Erscheint auch als Online-Ausgabe 978-1-4704-1273-9 Mathematical surveys and monographs 42 (DE-604)BV000018014 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006856934&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Freese, Ralph S. Ježek, Jaroslav Nation, J. B. 1948- Free lattices Mathematical surveys and monographs Gittertheorie (DE-588)4157394-8 gnd |
| subject_GND | (DE-588)4157394-8 |
| title | Free lattices |
| title_auth | Free lattices |
| title_exact_search | Free lattices |
| title_full | Free lattices Ralph Freese ; Jaroslav Ježek ; J. B. Nation |
| title_fullStr | Free lattices Ralph Freese ; Jaroslav Ježek ; J. B. Nation |
| title_full_unstemmed | Free lattices Ralph Freese ; Jaroslav Ježek ; J. B. Nation |
| title_short | Free lattices |
| title_sort | free lattices |
| topic | Gittertheorie (DE-588)4157394-8 gnd |
| topic_facet | Gittertheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006856934&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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