Preprimal algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Akademie-Verlag
1982
|
| Schriftenreihe: | Mathematical research
Band 11 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 162 Seiten |
Internformat
MARC
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| 100 | 1 | |a Denecke, Klaus |d 1944- |0 (DE-588)136447929 |4 aut | |
| 245 | 1 | 0 | |a Preprimal algebras |c by Klaus Denecke |
| 264 | 1 | |a Berlin |b Akademie-Verlag |c 1982 | |
| 300 | |a 162 Seiten | ||
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| 490 | 1 | |a Mathematical research |v Band 11 | |
| 650 | 4 | |a Algebra, Universal | |
| 650 | 4 | |a Many-valued logic | |
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Datensatz im Suchindex
| _version_ | 1810687774485905408 |
|---|---|
| adam_text |
Contents
Introduction H
1. Basic concepts 26
1.1 Functions on a finite set 26
1.2 Finite algebras 30
1.3 Varieties 34
1.4 Categorical algebras 37
1.5 Paraprinal and cryptoprimal algebras 39
1.6 On finite axiomatizability of finite algebras 41
2. Arithmetical varieties 42
2.1 Characterization of quasiprimal and functionally complete
algebras 42
2.2 A characterization of semiprimal, demiprimal, and primal
algebras 45
2.3 Hemiprimal algebras 49
2.4 Representation theorem ¦ 51
Problems and comments 52
3. Two element preprimal algebras 53
3.2 Two element algebras and varieties generated by
two element algebras 56
3.3 Completeness properties of two element algebras 63
Problems and comments 64
4. Preprimal algebras 65
4.1 Classification of all maximal classes of functions in F_(A) 65
4.2 Elementary properties of preprimal algebras 69
4.3 Independent sets and free preprimal algebras 72
4.4 Weak automorphisms of preprimal algebras 75
Problems and comments 79
5. Varieties generated by preprimal algebras 80
5.1 An algebraic characterization of preprimal algebras
generating arithmetical varieties 80
5.2 Preprimal algebras generating either congruence distributive
or congruence permutable varieties 83
5.3 Preprimal algebras generating neither congruence
distributive nor congruence permutable varieties 89
5.4 Algebraic characterization of preprimal algebras
generating 2 distributive varieties 91
5.5 Subdirectly irreducible elements, representation theorems 97
9
5.6 Equationally maximal preprimal algebras 108
5.7 Semidegenerate varieties generated by preprimal algebras 111
5.8 The lattice of subvarieties of a variety generated by a
preprimal algebra 114
5.9 On finite axiomatizability of preprimal algebras 117
Problems and comments 118
6. Completeness in universal algebras 119
6.1 Primality 119
6.2 Primality and preprimality of finite algebras with a
single fundamental operation 121
6.3 Functionally complete algebras 125
6.4 A new proof of Rosenberg's primal algebra characterization
theorem by R.W.Quackenbush 130
Problems and comments 131
7. Examples for preprimal algebras 132
Appendix: Quackenbush's new proof of Rosenberg's theorem 137
Bibliography 153
Subject Index 161
10 |
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| author | Denecke, Klaus 1944- |
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| classification_rvk | SK 130 SK 200 SK 320 |
| classification_tum | MAT 160f |
| ctrlnum | (OCoLC)10282844 (DE-599)BVBBV000249718 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre | Präprimale Algebra gnd |
| genre_facet | Präprimale Algebra |
| id | DE-604.BV000249718 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-20T04:27:05Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000150512 |
| oclc_num | 10282844 |
| open_access_boolean | |
| owner | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-91G DE-BY-TUM DE-384 DE-703 DE-739 DE-83 DE-11 DE-188 |
| physical | 162 Seiten |
| psigel | TUB-nvmb |
| publishDate | 1982 |
| publishDateSearch | 1982 |
| publishDateSort | 1982 |
| publisher | Akademie-Verlag |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Denecke, Klaus 1944- (DE-588)136447929 aut Preprimal algebras by Klaus Denecke Berlin Akademie-Verlag 1982 162 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical research Band 11 Algebra, Universal Many-valued logic Mehrwertige Logik (DE-588)4169335-8 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 gnd rswk-swf Algebraische Struktur (DE-588)4001166-5 s DE-604 Mehrwertige Logik (DE-588)4169335-8 s Mathematical research Band 11 (DE-604)BV000008585 11 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000150512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Denecke, Klaus 1944- Preprimal algebras Mathematical research Algebra, Universal Many-valued logic Mehrwertige Logik (DE-588)4169335-8 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| subject_GND | (DE-588)4169335-8 (DE-588)4001166-5 |
| title | Preprimal algebras |
| title_auth | Preprimal algebras |
| title_exact_search | Preprimal algebras |
| title_full | Preprimal algebras by Klaus Denecke |
| title_fullStr | Preprimal algebras by Klaus Denecke |
| title_full_unstemmed | Preprimal algebras by Klaus Denecke |
| title_short | Preprimal algebras |
| title_sort | preprimal algebras |
| topic | Algebra, Universal Many-valued logic Mehrwertige Logik (DE-588)4169335-8 gnd Algebraische Struktur (DE-588)4001166-5 gnd |
| topic_facet | Algebra, Universal Many-valued logic Mehrwertige Logik Algebraische Struktur |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000150512&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT deneckeklaus preprimalalgebras |