Distributive lattices:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Columbia, Mo.
Univ. of Missouri Press
1974
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 294 S. |
| ISBN: | 0826201636 |
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MARC
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| 245 | 1 | 0 | |a Distributive lattices |c Raymond Balbes and Philip Dwinger |
| 264 | 1 | |a Columbia, Mo. |b Univ. of Missouri Press |c 1974 | |
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| 650 | 7 | |a Treillis distributifs |2 ram | |
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Record in the Search Index
| _version_ | 1804117366901047296 |
|---|---|
| adam_text | Contents
Preface, ix
Acknowledgments, xiii
I. Preliminaries, 1
Part 1. Foundations
1. Basic definitions and terminology, 1
2. Partially ordered sets, 3
3. Ordinals and cardinals, 4
Part 2. Universal Algebra
4. Algebras and homomorphisms, 6
5. Direct products, 8
6. Congruence relations, 9
7. Classes of algebras, 10
8. The duality principles, 12
9. Subdirect products, 13
10. Free algebras, 14
11. Polynomials and identities, 15
12. Birkhoff s characterization of equational classes, 17
Part 3. Categories
13. Definition of a category, 20
14. Special morphisms, 21
15. Products and coproducts. Limits and colimits, 23
16. Injectives andprojectives, 24
17. Functors, 25
18. Reflective subcategories, 27
19. Categories of algebras, 30
20. Equational categories, 31
II. Lattices
1. Partially ordered sets {continued), 39
2. Definition of a lattice, 42
3. Lattices as algebras and categories, 43
4. Complete lattices and closure operators, 45
5. The distributive law, 48
6. Complements, Boolean algebras, 51
7. Relatively complemented distributive lattices, 54
8. 27ze various categories, 56
9. Ideals and congruence relations, 57
10. Subdirect product representation for distributive lattices, 63
III. The Prime Ideal Theorem
1. Irreducible elements, 65
2. 7%e descending chain condition, 66
3. Prime ideals and maximal ideals, 67
4. The prime ideal theorem, 70
5. Representation by sets, 71
6. Some corollaries of the prime ideal theorem, 72
IV. Topological Representations
1. Stone spaces, 75
2. Topological representation theory for Qln, 79
3. Topological representation theory for 0$, 81
V. Extension Properties
1. Subalgebras generated by sets, 85
2. Extending functions to homomorphisms, 86
3. Free algebras, 88
4. Free Boolean extensions, 97
5. Embedding of relatively complemented distributive lattices in Boolean algebras, 101
6. Free relatively complemented distributive extensions, 102
7. Boolean algebras generated by a chain. Countable Boolean algebras, 105
8. Monomorphisms andepimbrphisms, 109
9. Injectives in ), gitl and3$, 112
10. Weakprojectivesin3 and@lu, 114
VI. Subdirect Products of Chains
. Introduction, 119
2. Definitions, some basic theorems, and an example, 120
3. Basic K chains, 121
4. The classes Cnfor n 3. Locally separatedn chains, 122
5. The class Cs, 125
6. ^4 structure theorem for Q, 127
7. Maximal ideals and Nachbin s theorem, 129
8. Subdirect products of infinite chains, 130
VII. Coproducts and Colimits
1. Existence and characterization of coproducts in 2, ®01 andffl, 132
2. The coproduct convention, 135
3. The center of the coproduct in ®oi, 136
4. Structure theorems for coproducts of Boolean algebras and chains, 138
5. Rigid chains, 142
6. Uniqueness of representation of coproducts of Boolean algebras and chains, 144
7. 77*e representation space of coproducts in Sin and 38,147
8. Colimits, 149
VUL Pseudocomplemented Distributive Lattices
1. Definitions and examples, 151
2. Basic properties, 153
3. The class B^, 155
4. Glivenkd s theorem and some implications, 156
5. Subdirectly irreducible algebras in Bu, 159
6. The equationalsubclasses of Ba, 161
7. Stone algebras, 164
8. Injective Stone algebras, 168
9. Coproducts of Stone algebras. Free Stone algebras, 171
IX. Heyting Algebras
1. Introduction, 173
2. Definitions, 173
3. Examples, 177
4. The class H, 111
5. Some fundamental theorems, 179
6. Free Heyting algebras, 182
7. jFiH/Ve weakly projective Heyting algebras, 185
X. Post Algebras
1. Introduction, 191
2. Definitions and basic properties, 192
3. The category of Post algebras, 195
4. Representation theory, 197
5. The partially ordered set of prime ideals of a Post algebra, 198
6. Post algebras as equational classes of algebras, 200
7. Coproducts in ^n and free Post algebras, 202
8. Generalized Post algebras, 203
9. Stone algebras of order n, 205
XI. De Morgan Algebras and Lukasiewicz Algebras
1. Introduction, 211
2. De Morgan algebras. Basic properties and representation theory, 1 1
3. Equational subclasses ofM, 215
4. Coproducts ofde Morgan algebras. Free de Morgan algebras, 216
5. Lukasiewicz algebras. Definitions and basic theorems, 218
6. Pas? algebras as special cases of Lukasiewicz algebras, 221
7. ^4 representation theory for Lukasiewicz algebras, 223
8. The partially ordered set of prime ideals of a Lukasiewicz algebra, 224
9. Embedding of Lukasiewicz algebras in Post algebras. Infective objects in ^PB, 224
10. Free Lukasiewicz algebras, 226
XII. Complete and a Complete Distributive Lattices
1. Introduction. Definitions and some theorems, 228
2. Normal completion of lattices. The special case of distributive lattices, 233
3. The normal completion of a Boolean algebra, 240
4. Complete, completely distributive lattices, 243
5. Representation of distributive, a complete lattices, 250
Bibliography, 261
Index of Authors and Terms, 284
Index of Symbols, 292
|
| any_adam_object | 1 |
| author | Balbes, Raymond Dwinger, Philip 1914-2006 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511/.33 |
| dewey-search | 511/.33 |
| dewey-sort | 3511 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV003077838 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:53:16Z |
| institution | BVB |
| isbn | 0826201636 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001929661 |
| oclc_num | 490262804 |
| open_access_boolean | |
| owner | DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-83 DE-188 |
| owner_facet | DE-384 DE-739 DE-355 DE-BY-UBR DE-824 DE-29T DE-19 DE-BY-UBM DE-83 DE-188 |
| physical | XIII, 294 S. |
| publishDate | 1974 |
| publishDateSearch | 1974 |
| publishDateSort | 1974 |
| publisher | Univ. of Missouri Press |
| record_format | marc |
| spelling | Balbes, Raymond Verfasser aut Distributive lattices Raymond Balbes and Philip Dwinger Columbia, Mo. Univ. of Missouri Press 1974 XIII, 294 S. txt rdacontent n rdamedia nc rdacarrier Treillis distributifs ram Lattices, Distributive Verbandstheorie (DE-588)4127072-1 gnd rswk-swf Verbandstheorie (DE-588)4127072-1 s DE-604 Dwinger, Philip 1914-2006 Verfasser (DE-588)117709646 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001929661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balbes, Raymond Dwinger, Philip 1914-2006 Distributive lattices Treillis distributifs ram Lattices, Distributive Verbandstheorie (DE-588)4127072-1 gnd |
| subject_GND | (DE-588)4127072-1 |
| title | Distributive lattices |
| title_auth | Distributive lattices |
| title_exact_search | Distributive lattices |
| title_full | Distributive lattices Raymond Balbes and Philip Dwinger |
| title_fullStr | Distributive lattices Raymond Balbes and Philip Dwinger |
| title_full_unstemmed | Distributive lattices Raymond Balbes and Philip Dwinger |
| title_short | Distributive lattices |
| title_sort | distributive lattices |
| topic | Treillis distributifs ram Lattices, Distributive Verbandstheorie (DE-588)4127072-1 gnd |
| topic_facet | Treillis distributifs Lattices, Distributive Verbandstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001929661&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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