Polynomial completeness in algebraic systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 358 S. |
| ISBN: | 1584882034 |
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MARC
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Record in the Search Index
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| adam_text | POLYNOMIAL COMPLETENESS IN ALGEBRAIC SYSTEMS KALLE KAARLI ALDEN F.
PIXLEY CHAPMAN & HALL/CRC BOCA RATON LONDON NEW YORK WASHINGTON, D.C.
CONTENTS ALGEBRAS, LATTICES, AND VARIETIES 1 1.1 ALGEBRAS, LANGUAGES,
CLONES, VARIETIES 1 1.1.1 ALGEBRAS 1 1.1.2 LANGUAGES AND STRUCTURES 5
1.1.3 CLONES AND RELATED TOPICS 13 1.1.4 VARIETIES 23 1.2 CONGRUENCE
PROPERTIES 27 1.2.1 MAL CEV CONDITIONS 27 1.2.2 DEFINABLE PRINCIPAL
CONGRUENCES 36 1.2.3 NEAR UNANIMITY OPERATIONS AND CONGRUENCE
DISTRIBUTIVITY 44 1.2.4 CONGRUENCE PERMUTABILITY AND RECTANGULAR
SUBALGEBRAS 46 1.2.5 CONGRUENCE DISTRIBUTIVITY AND SKEW CONGRUENCES 49
1.2.6 THE COMMUTATOR 58 CHARACTERIZATIONS OF EQUIVALENCE LATTICES 65 2.1
INTRODUCTION 65 2.2 ARITHMETICITY 67 2.2.1 THE STRONG CHINESE REMAINDER
CONDITION FOR EQUIVALENCE LATTICES 68 2.2.2 THE COMPATIBLE FUNCTION
EXTENSION PROPERTY . . 69 2.2.3 EXISTENCE OF COMPATIBLE PIXLEY FUNCTIONS
. . . . 71 2.2.4 APPLICATIONS OF PRINCIPAL PIXLEY FUNCTIONS ... 78 2.2.5
COMPATIBLE CHOICE FUNCTIONS 86 2.3 COMPATIBLE FUNCTION LIFTING 88 2.3.1
COMPATIBLE FUNCTION LIFTING IMPLIES DISTRIBUTIVITY (FINITE CASE) 91 VI
CONTENTS 2.3.2 COMPATIBLE FUNCTION LIFTING IMPLIES COMPATIBLE FUNCTION
SYSTEM EXTENSION 94 2.3.3 COMPATIBLE FUNCTION LIFTING IMPLIES
DISTRIBUTIVITY (RESIDUALLY FINITE CASE) 101 3 PRIMALITY AND
GENERALIZATIONS 107 3.1 PRIMALITY AND FUNCTIONAL COMPLETENESS 107 3.1.1
PRIMALITY 107 3.1.2 HISTORY: POST ALGEBRAS 109 3.1.3 PRIMALITY AND
FUNCTIONAL COMPLETENESS: CHARACTERIZATIONS ILL 3.1.4 FUNCTIONALLY
COMPLETE ALGEBRAS 120 3.2 NEAR UNANIMITY VARIETIES 128 3.2.1
CHARACTERIZATIONS 128 3.2.2 MORE PROPERTIES OF NEAR UNANIMITY VARIETIES
. . 133 3.3 ARITHMETICAL VARIETIES 137 3.4 GENERALIZATIONS OF PRIMALITY
141 3.4.1 GENERALIZATIONS INVOLVING TERM FUNCTION CHARACTERIZATIONS 141
3.4.2 AFFINE COMPLETE ALGEBRAS 157 3.4.3 POLYNOMIAL INTERPOLATION 161
3.5 CATEGORICAL EQUIVALENCE 165 4 AFFINE COMPLETE VARIETIES 173 4.1
INTRODUCTION AND INSTRUCTIVE EXAMPLES 173 4.2 GENERAL PROPERTIES 177 4.3
VARIETIES WITH A FINITE RESIDUAL BOUND 182 4.3.1 SOME CATEGORICAL
PROPERTIES 182 4.3.2 PROPERTY (S) 184 4.3.3 TWO COUNTER-EXAMPLES 188 4.4
LOCALLY FINITE AFFINE COMPLETE VARIETIES 193 4.4.1 EXISTENCE OF A NEAR
UNANIMITY TERM 193 4.4.2 STRUCTURE THEOREMS 195 4.4.3 THE ARITHMETICAL
CASE 201 4.4.4 EXAMPLES 210 4.4.5 CATEGORICAL EQUIVALENCE 218 CONTENTS
VII 5 POLYNOMIAL COMPLETENESS IN SPECIAL VARIETIES 221 5.1 STRICTLY
LOCALLY AFFINE COMPLETE ALGEBRAS 221 5.1.1 INTERPOLATION AND THE CLASS
SPJ(A) 221 5.1.2 NEUTRALITY 226 5.2 MODULES 232 5.2.1 GENERAL
OBSERVATIONS 232 5.2.2 COMPLETENESS OF WEAK DIRECT POWERS 235 5.2.3
SEMISIMPLE MODULES AND SEMISIMPLE RINGS . . . 240 5.2.4 ABELIAN GROUPS
244 5.3 LATTICES 254 5.3.1 GENERAL OBSERVATIONS 254 5.3.2 DISTRIBUTIVE
LATTICES 257 5.3.3 ORDER AFFINE COMPLETENESS OF LATTICES 266 5.3.4 ORDER
FUNCTIONALLY COMPLETE LATTICES 280 5.4 ALGEBRAS BASED ON DISTRIBUTIVE
LATTICES 285 5.4.1 LATTICES AFFINE COMPLETE IN A DISTRIBUTIVE LATTICE
286 5.4.2 STONE ALGEBRAS 289 5.4.3 KLEENE ALGEBRAS 296 5.5 SEMILATTICES
306 5.5.1 COMPATIBLE FUNCTIONS ON SEMILATTICES 306 5.5.2 COMPLETENESS
THEOREMS 314 5.6 MISCELLANEOUS RESULTS 317 5.6.1 P-RINGS AND SUBALGEBRA
PRIMAL ALGEBRAS 317 5.6.2 MEDIAN ALGEBRAS 322 5.6.3 COMMUTATIVE INVERSE
SEMIGROUPS 326 5.6.4 LATTICE ORDERED GROUPS 330 BIBLIOGRAPHY 333 INDEX
351
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| any_adam_object | 1 |
| author | Kaarli, Kalle Pixley, Alden F. |
| author_facet | Kaarli, Kalle Pixley, Alden F. |
| author_role | aut aut |
| author_sort | Kaarli, Kalle |
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| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Kaarli, Kalle Verfasser aut Polynomial completeness in algebraic systems Kalle Kaarli ; Alden F. Pixley Boca Raton [u.a.] CRC Press 2001 XV, 358 S. txt rdacontent n rdamedia nc rdacarrier Polinomios Teorema de la completitud Pixley, Alden F. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009082793&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaarli, Kalle Pixley, Alden F. Polynomial completeness in algebraic systems Polinomios Teorema de la completitud |
| title | Polynomial completeness in algebraic systems |
| title_auth | Polynomial completeness in algebraic systems |
| title_exact_search | Polynomial completeness in algebraic systems |
| title_full | Polynomial completeness in algebraic systems Kalle Kaarli ; Alden F. Pixley |
| title_fullStr | Polynomial completeness in algebraic systems Kalle Kaarli ; Alden F. Pixley |
| title_full_unstemmed | Polynomial completeness in algebraic systems Kalle Kaarli ; Alden F. Pixley |
| title_short | Polynomial completeness in algebraic systems |
| title_sort | polynomial completeness in algebraic systems |
| topic | Polinomios Teorema de la completitud |
| topic_facet | Polinomios Teorema de la completitud |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009082793&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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