Lattices and ordered algebraic structures:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
2005
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | IX, 303 S. |
| ISBN: | 1852339055 |
Staff View
MARC
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| 100 | 1 | |a Blyth, Thomas S. |d 1938- |e Verfasser |0 (DE-588)115496076 |4 aut | |
| 245 | 1 | 0 | |a Lattices and ordered algebraic structures |c T. S. Blyth |
| 264 | 1 | |a London |b Springer |c 2005 | |
| 300 | |a IX, 303 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Structures algébriques ordonnées | |
| 650 | 4 | |a Treillis, Théorie des | |
| 650 | 4 | |a aOrdered algebraic structures | |
| 650 | 4 | |a aLattice theory | |
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Record in the Search Index
| _version_ | 1804133037412188160 |
|---|---|
| adam_text | Contents
Ordered sets; residuated mappings
......................... 1
1.1
The concept of an order
.................................. 1
1.2
Order-preserving mappings
............................... 5
1.3
Residuated mappings
.................................... 6
1.4
Closures
................................................ 10
1.5
Isomorphisms of ordered sets
.............................. 12
1.6
Galois connections
....................................... 14
1.7
Semigroups of residuated mappings
........................ 15
Lattices; lattice morphisms
................................ 19
2.1
Semilattices and lattices
.................................. 19
2.2
Down-set lattices
........................................ 23
2.3
Sublattices
............................................. 26
2.4
Lattice morphisms
....................................... 28
2.5
Complete lattices
........................................ 29
2.6
Baer semigroups
......................................... 35
Regular equivalences
...................................... 39
3.1
Ordering quotient sets
................................... 39
3.2
Strongly upper regular equivalences
........................ 41
3.3
Lattice congruences
...................................... 45
Modular lattices
........................................... 49
4.1
Modular pairs; Dedekind s modularity criterion
.............. 49
4.2
Chain conditions
........................................ 54
4.3
Join-irreducibles
......................................... 58
4.4
Baer semigroups and modularity
.......................... 61
Distributive lattices
....................................... 65
5.1
Birkhoff s distributivity criterion
.......................... 65
5.2
More on join-irreducibles
................................. 69
5.3
Prime ideals and filters
................................... 72
5.4
Baer semigroups and distributivity
........................ 74
6
Complementation; boolean algebras
....................... 77
6.1
Complemented elements
.................................. 77
6.2
Uniquely complemented lattices
........................... 78
6.3
Boolean algebras and boolean rings
........................ 82
6.4
Boolean algebras of subsets
............................... 86
6.5
The Dedekind-MacNeille completion of a boolean algebra
.... 90
6.6
Neutral and central elements
.............................. 92
6.7
Stone s representation theorem
............................ 95
6.8
Baer semigroups and complementation
..................... 97
6.9
Generalisations of boolean algebras
........................101
7
Pseudocomplementation; Stone and Heyting algebras
......103
7.1
Pseudocomplements
.....................................103
7.2
Stone algebras
..........................................106
7.3
Heyting algebras
........................................
Ill
7.4
Baer semigroups and residuation
..........................116
8
Congruences; subdirectly irreducible algebras
..............119
8.1
More on lattice congruences
..............................119
8.2
Congruence kernels
......................................121
8.3
Principal congruences
....................................126
8.4
Congruences on p-algebras
................................130
8.5
Congruences on Heyting algebras
..........................134
8.6
Subdirectly irreducible algebras
...........................137
9
Ordered groups
............................................143
9.1
Ordering groups
.........................................143
9.2
Convex subgroups
.......................................147
9.3
Lattice-ordered groups
...................................150
9.4
Absolute values and orthogonality
.........................153
9.5
Convex ¿-subgroups
.......................................158
9.6 Polars..................................................162
9.7
Coset ordering; prime subgroups
..........................164
9.8
Representable groups
....................................168
10
Archimedean ordered structures
...........................171
10.1
Totally ordered rings and fields
............................171
10.2
Archimedean ordered fields
...............................177
10.3
Archimedean totally ordered groups
.......................188
11
Ordered semigroups; residuated semigroups
...............193
11.1
Ordered semigroups
......................................193
11.2
Residuated semigroups
...................................197
11.3
Molinaio
equivalences
....................................204
12
Epimorphic group images; Dubreil-Jacotin semigroups
.....207
12.1
Anticones
..............................................207
12.2
Dubreil-Jacotin semigroups
...............................212
12.3
Residuated Dubreil-Jacotin semigroups
.....................217
13
Ordered regular semigroups
...............................225
13.1
Regular Dubreil-Jacotin semigroups
........................225
13.2
The Nambooripad order
..................................228
13.3
Natural orders on regular semigroups
......................232
13.4
Biggest inverses
.........................................243
13.5
Principally ordered regular semigroups
.....................251
13.6
Principally and naturally ordered semigroups
...............255
13.7
Ordered completely simple semigroups
.....................258
14
Structure theorems
........................................265
14.1
Naturally ordered regular semigroups
......................265
14.1.1
Inverse transversals
................................265
14.1.2
Biggest idempotent
................................269
14.1.3
Biggest inverses
...................................269
14.2
Integral Dubreil-Jacotin inverse semigroups
.................271
14.3
Orthodox Dubreil-Jacotin semigroups
......................274
14.3.1
The cartesian order
................................276
14.3.2
Unilateral lexicographic orders
......................282
14.3.3
Bootlace orders
...................................285
14.3.4
Lexicographic orders
...............................290
14.4
Lattices for which Res
L
is regular
.........................291
References
.....................................................293
Index
..........................................................299
|
| any_adam_object | 1 |
| author | Blyth, Thomas S. 1938- |
| author_GND | (DE-588)115496076 |
| author_facet | Blyth, Thomas S. 1938- |
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| dewey-full | 511.3/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/3 |
| dewey-search | 511.3/3 |
| dewey-sort | 3511.3 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019658730 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:02:21Z |
| institution | BVB |
| isbn | 1852339055 |
| language | English |
| lccn | 2004056612 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012987179 |
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| physical | IX, 303 S. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Blyth, Thomas S. 1938- Verfasser (DE-588)115496076 aut Lattices and ordered algebraic structures T. S. Blyth London Springer 2005 IX, 303 S. txt rdacontent n rdamedia nc rdacarrier Universitext Includes bibliographical references and index Structures algébriques ordonnées Treillis, Théorie des aOrdered algebraic structures aLattice theory Verbandstheorie (DE-588)4127072-1 gnd rswk-swf Geordnete algebraische Struktur (DE-588)4156743-2 gnd rswk-swf Verbandstheorie (DE-588)4127072-1 s Geordnete algebraische Struktur (DE-588)4156743-2 s DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012987179&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blyth, Thomas S. 1938- Lattices and ordered algebraic structures Structures algébriques ordonnées Treillis, Théorie des aOrdered algebraic structures aLattice theory Verbandstheorie (DE-588)4127072-1 gnd Geordnete algebraische Struktur (DE-588)4156743-2 gnd |
| subject_GND | (DE-588)4127072-1 (DE-588)4156743-2 |
| title | Lattices and ordered algebraic structures |
| title_auth | Lattices and ordered algebraic structures |
| title_exact_search | Lattices and ordered algebraic structures |
| title_full | Lattices and ordered algebraic structures T. S. Blyth |
| title_fullStr | Lattices and ordered algebraic structures T. S. Blyth |
| title_full_unstemmed | Lattices and ordered algebraic structures T. S. Blyth |
| title_short | Lattices and ordered algebraic structures |
| title_sort | lattices and ordered algebraic structures |
| topic | Structures algébriques ordonnées Treillis, Théorie des aOrdered algebraic structures aLattice theory Verbandstheorie (DE-588)4127072-1 gnd Geordnete algebraische Struktur (DE-588)4156743-2 gnd |
| topic_facet | Structures algébriques ordonnées Treillis, Théorie des aOrdered algebraic structures aLattice theory Verbandstheorie Geordnete algebraische Struktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012987179&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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