Finitely generated commutative monoids:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Commack, NY
Nova Science Publ.
1999
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 185 S. |
| ISBN: | 1560726709 |
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MARC
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Record in the Search Index
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| adam_text | FINITELY GENERATED COMMUTATIVE MONOIDS J. C. ROSALES AND P. A.
GARCIA-SANCHEZ NOVA SCIENCE PUBLISHERS, INC. COMMACK, NEW YORK CONTENTS
PREFACE IX ACKNOWLEDGEMENTS XIII CHAPTER 1. BASIC DEFINITIONS AND
RESULTS 1 REMARKS - 6 EXERCISES 6 CHAPTER 2. FINITELY GENERATED
COMMUTATIVE GROUPS 9 1. BASES AND RANK OF A SUBGROUP OF Z N 9 2.
EQUIVALENCE OF MATRICES WITH INTEGER ENTRIES AND INVARIANT FACTORS 12 3.
SOME PRACTICAL RESULTS CONCERNING THE COMPUTATION OF A BASIS 20 REMARKS
23 EXERCISES 23 CHAPTER 3. FINITELY GENERATED CANCELLATIVE MONOIDS 25 1.
FINITELY GENERATED CANCELLATIVE TORSION FREE MONOIDS 27 2. FINITELY
GENERATED CANCELLATIVE REDUCED MONOIDS 28 3. FINITE CANCELLATIVE MONOIDS
32 REMARKS 33 EXERCISES 33 CHAPTER 4. MINKOWSKI-FARKAS LEMMA AND ITS
APPLICATIONS TO MONOIDS 35 1. MAIN RESULT AND ALGORITHMS 35 2.
APPLICATIONS TO MONOIDS 41 REMARKS 45 EXERCISES 45 CHAPTER 5. FINITELY
GENERATED MONOIDS ARE FINITELY PRESENTED 47 1. LINEAR ADMISSIBLE ORDERS
47 2. RE DEI S THEOREM 50 3. THE WORD PROBLEM FOR MONOIDS 52 4. CYCLIC
MONOIDS 53 REMARKS 54 EXERCISES 54 CHAPTER 6. THE WORD PROBLEM FOR
MONOIDS 57 1. REDUCED SYSTEMS OF GENERATORS OF A CONGRUENCE 57 2.
CANONICAL SYSTEMS OF GENERATORS OF A CONGRUENCE 59 3. THE GROUP OF UNITS
OF A MONOID 65 REMARKS 69 EXERCISES 70 CHAPTER 7. NONNEGATIVE INTEGER
SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS 73 1. NONNEGATIVE INTEGER
SOLUTIONS OF A SYSTEM OF LINEAR HOMOGENEOUS DIOPHANTINE EQUATIONS 73 2.
THE MONOID OF NONNEGATIVE ELEMENTS OF A SUBGROUP OF Z 77 3. NONNEGATIVE
INTEGER SOLUTIONS OF SYSTEMS OF LINEAR DIOPHANTINE EQUATIONS 80 4.
NORMAL AFFINE SEMIGROUPS 81 REMARKS 83 EXERCISES 84 CHAPTER 8. COMPUTING
PRESENTATIONS OF FINITELY GENERATED CANCELLATIVE MONOIDS 85 1. PRIMITIVE
ELEMENTS OF A CONGRUENCE 85 2. COMPUTING PRESENTATIONS OF FINITELY
GENERATED CANCELLATIVE MONOIDS 87 3. DECIDING WHETHER A MONOID IS
CANCELLATIVE 90 REMARKS 91 EXERCISES 91 CHAPTER 9. MINIMAL PRESENTATIONS
OF FINITELY GENERATED CANCELLATIVE REDUCED MONOIDS 93 1.
CHARACTERIZATION OF MINIMAL PRESENTATIONS OF FINITELY GENERATED
CANCELLATIVE REDUCED MONOIDS 93 2. THE AFFINE CASE 96 REMARKS 102
EXERCISES 103 CHAPTER 10. NUMERICAL SEMIGROUPS 105 1. MINIMAL
PRESENTATIONS OF NUMERICAL SEMIGROUPS 108 2. A BOUND FOR THE CARDINALITY
OF MINIMAL PRESENTATIONS OF NUMERICAL SEMIGROUPS 110 3. NUMERICAL
SEMIGROUPS WITH MAXIMAL EMBEDDING DIMENSION 113 REMARKS 116 EXERCISES
117 CHAPTER 11. PROJECTIONS OF CONGRUENCES 119 1. PRESENTATIONS OF
FINITELY GENERATED CANCELLATIVE MONOIDS AS PROJECTIONS OF AFFINE
SEMIGROUPS 119 2. LIFTING SOME PROJECTIONS 123 REMARKS 127 EXERCISES 127
CHAPTER 12. FINITE TORSION FREE MONOIDS 129 1. PRESENTATIONS OF FINITE
TORSION FREE MONOIDS 129 2. FINITE LATTICES 130 3. FINITE BOOLEAN
ALGEBRAS 133 4. BOOLEAN MONOIDS 137 REMARKS 139 EXERCISES 140 CHAPTER
13. ARCHIMEDEAN COMPONENTS 143 1. COMPUTING THE ARCHIMEDEAN COMPONENTS
OF A FINITELY GENERATED MONOID 145 REMARKS 150 EXERCISES 150 CHAPTER 14.
SEPARATIVE MONOIDS 153 1. SEPARATIVE MONOIDS AND THEIR ARCHIMEDEAN
COMPONENTS 153 2. DECIDING WHETHER THE QUOTIENT OF AN IDEAL OF W BY A
CONGRUENCE IS CANCELLATIVE 155 3. ELIMINATION 158 4. DECIDING WHETHER A
FINITELY GENERATED MONOID IS SEPARATIVE 158 5. DECIDING WHETHER A
FINITELY GENERATED MONOID IS TORSION FREE 160 6. ^-SEMIGROUPS 162
REMARKS 167 EXERCISES 167 APPENDIX A. GRAPHS 169 BIBLIOGRAPHY . 1 7 1
INDEX OF NOTATION 175 INDEX OF MAIN RESULTS AND ALGORITHMS 177 INDEX 183
|
| any_adam_object | 1 |
| author | Rosales, J. C. García-Sánchez, P. A. |
| author_facet | Rosales, J. C. García-Sánchez, P. A. |
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| spelling | Rosales, J. C. Verfasser aut Finitely generated commutative monoids J. C. Rosales and P. A. García-Sánchez Commack, NY Nova Science Publ. 1999 XII, 185 S. txt rdacontent n rdamedia nc rdacarrier Commutative algebra Monoids Semigroups García-Sánchez, P. A. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008543273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosales, J. C. García-Sánchez, P. A. Finitely generated commutative monoids Commutative algebra Monoids Semigroups |
| title | Finitely generated commutative monoids |
| title_auth | Finitely generated commutative monoids |
| title_exact_search | Finitely generated commutative monoids |
| title_full | Finitely generated commutative monoids J. C. Rosales and P. A. García-Sánchez |
| title_fullStr | Finitely generated commutative monoids J. C. Rosales and P. A. García-Sánchez |
| title_full_unstemmed | Finitely generated commutative monoids J. C. Rosales and P. A. García-Sánchez |
| title_short | Finitely generated commutative monoids |
| title_sort | finitely generated commutative monoids |
| topic | Commutative algebra Monoids Semigroups |
| topic_facet | Commutative algebra Monoids Semigroups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008543273&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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