Residuated structures with involution:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Aachen
Shaker
2006
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| Series: | Berichte aus der Mathematik
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 162 S. graph. Darst. |
| ISBN: | 3832257896 |
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| adam_text | RESIDUATED STRUCTURES WITH INVOLUTION VOM FACHBEREICH MATHEMATIK DER
TECHNISCHEN UNIVERSITAET DARMSTADT ZUR ERLANGUNG DES GRADES EINES DOKTORS
DER NATURWISSENSCHAFTEN (DR. RER. NAT.) GENEHMIGTE DISSERTATION VON
DIPL.-MATH. ANNIKA MEIKE WILLE AUS KASSEL REFERENT: PROF. DR. C.
HERRMANN KOREFERENT: PROF. DR. D. MUNDICI KOREFERENT: PROF. DR. M. OTTO
KOREFERENT: PROF. DR. C. TSINAKIS TAG DER EINREICHUNG: 8. JUNI 2006 TAG
DER MUENDLICHEN PRUEFUNG: 21. JULI 2006 DARMSTADT 2006 D17 CONTENTS 1.
INTRODUCTION 1 2. PRELIMINARIES 5 2.1. UNIVERSAL ALGEBRA 5 2.1.1.
FIRST-ORDER STRUCTURES, TERMS AND FORMULAS 5 2.1.2. LATTICES 7 2.1.3.
CONGRUENCES AND HOMOMORPHISMS ... 8 2.1.4. REDUCED PRODUCTS AND
ULTRAPRODUCTS . . 11 2.1.5. VARIETIES AND QUASIVARIETIES 12 2.1.6. FREE
ALGEBRAS 13 2.1.7. ELEMENTARY DASSES AND FINITE AXIOMATIZ- ABILITY 13
2.1.8. SUBDIRECT PRODUCTS 15 2.1.9. JOENSSON S LEMMA 16 2.1.10.
EQUATIONAL THEORY 16 2.2. RESIDUATED LATTICES 22 2.2.1. DEFINITION 22
2.2.2. BASIC PROPERTIES 24 2.2.3. STRUCTURE THEORY OFRC 26 3. POINTED
RESIDUATED LATTICES 35 3.1. WEAKLY INVOLUTIVE RESIDUATED LATTICES 36
3.2. INVOLUTIVE RESIDUATED LATTICES 37 3.3. BASIC PROPERTIES OF WEAKLY
INVOLUTIVE RESIDUATED LATTICES 39 IV CONTENTS 3.4. EXAMPLES OF WEAKLY
INVOLUTIVE RESIDUATED LATTICES 41 3.4.1. FINITE EXAMPLES 41 3.4.2.
BOOLEAN ALGEBRAS 46 3.4.3. LATTICE-ORDERED GROUPS 47 3.4.4. BOUNDED
GENERALIZED MV-ALGEBRAS.... 48 3.4.5. MV-ALGEBRAS 56 3.4.6. REDUCTS OF
RELATION ALGEBRAS 57 3.5. SUBVARIETYLATTICEOFWXN7?. 60 3.6. STRUCTURE
THEORY OF PTTC AND ITS SUBVARIETIES . . 61 3.7. FULLY INVARIANT NORMAL
FILTERS OF POINTED RESIDU- ATED LATTICES 64 3.8. DEDEKIND-MACNEILLE
COMPLETION 66 4. MINIMAL VARIETIES OF TRIRC 69 4.1. THE ATOMIC STRUCTURE
OFL(72.) 69 4.2. FROM MODULES TO INVOLUTIVE RESIDUATED LATTICES . 71
4.3. AN UNCOUNTABLE FAMILY OF INVOLUTIVE RESIDUATED LATTICES 77 4.4. THE
ATOMIC STRUCTURE OFL(I7?.) 81 5. A LATTICE EMBEDDING INTO INVOLUTIVE
RESID- UATED LATTICES 89 5.1. A LATTICE EMBEDDING INTO INVOLUTIVE
RESIDUATED LATTICES 90 5.2. ABOUTTHE STRUCTURE OFL(XW7?.) 95 5.3.
FINITE HEIGHT CONJECTURE 97 5.4. MODULAR INVOLUTIVE RESIDUATED LATTICES
97 5.4.1. DECIDABILITY PROBLEMS OF CERTAIN SUBVA- RIETIES OILNRC 98
5.4.2. UNDECIDABILITY OF THE EQUATIONAL THEORY OIMODLNUC 99 CONTENTS
5.5. FINITE AXIOMATIZABILITY OF VARIOUS INVOLUTIVE RESID- UATED LATTICE
VARIETIES 99 5.5.1. PRESERVATION BY ULTRAPRODUCTS 99 5.5.2. APPLICATION
OF MODULAR LATTICE RESULTS .. 102 5.5.3. FURTHER CONSEQUENCES 104 6. A
GENTZEN SYSTEM FOR INVOLUTIVE RESIDU- ATED LATTICES 1O7 6.1. INVOLUTIVE
NORMAL FORM 108 6.2. GIRARD QUANTALES 109 6.3. GENTZEN SYSTEM 110 6.4.
SOUNDNESS AND COMPLETENESS 113 7. THE FEP FOR INVOLUTIVE RESIDUATED
LATTICES 125 7.1. PRELIMINARIES 125 7.2. THE FINITE EMBEDDABILITY
PROPERTY FOR XTZC . . . 126 7.3. THE FINITE EMBEDDABILITY PROPERTY FOR
ILNTZC . . 128 7.4. FAILUREOFTHEFEPFORXNFT 130 8. THE WORD PROBLEM FOR
VARIOUS RESIDUATED LATTICE VARIETIES 133 8.1. PRELIMINARIES 133 8.2.
PRESENTATIONS AND THE WORD PROBLEM 134 8.3. THE INTERPRETATION TECHNIQUE
136 8.4. GENERALIZATION OFGROUP RESULTS 138 8.5. EXPANDING THE POWER SET
MONOID OF A GROUP ... 141 8.6. CONCLUSION 143 A. CONSTRUCTING FINITE
EXAMPLES WITH GAP 145 A.I. PROGRAM FILES 145 A.2. SELECTED FUNCTIONS 146
|
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| dewey-full | 511.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.33 |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T21:37:06Z |
| institution | BVB |
| isbn | 3832257896 |
| language | English |
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| physical | VI, 162 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
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| publisher | Shaker |
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| series2 | Berichte aus der Mathematik |
| spelling | Wille, Annika Meike 1976- Verfasser (DE-588)13260700X aut Residuated structures with involution Annika Meike Wille Aachen Shaker 2006 VI, 162 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Berichte aus der Mathematik Zugl.: Darmstadt, Techn. Univ., Diss., 2006 Verband Mathematik (DE-588)4062565-5 gnd rswk-swf Algebra mit Involution (DE-588)4236038-9 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Algebra mit Involution (DE-588)4236038-9 s Verband Mathematik (DE-588)4062565-5 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017442949&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wille, Annika Meike 1976- Residuated structures with involution Verband Mathematik (DE-588)4062565-5 gnd Algebra mit Involution (DE-588)4236038-9 gnd |
| subject_GND | (DE-588)4062565-5 (DE-588)4236038-9 (DE-588)4113937-9 |
| title | Residuated structures with involution |
| title_auth | Residuated structures with involution |
| title_exact_search | Residuated structures with involution |
| title_full | Residuated structures with involution Annika Meike Wille |
| title_fullStr | Residuated structures with involution Annika Meike Wille |
| title_full_unstemmed | Residuated structures with involution Annika Meike Wille |
| title_short | Residuated structures with involution |
| title_sort | residuated structures with involution |
| topic | Verband Mathematik (DE-588)4062565-5 gnd Algebra mit Involution (DE-588)4236038-9 gnd |
| topic_facet | Verband Mathematik Algebra mit Involution Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017442949&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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