Numerical semigroups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2009
|
| Schriftenreihe: | Developments in Mathematics
20 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 181 S. 235 mm x 155 mm |
| ISBN: | 9781441901590 |
Internformat
MARC
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| 100 | 1 | |a Rosales, José C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical semigroups |c by J. C. Rosales ; P. A. García-Sánchez |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2009 | |
| 300 | |a IX, 181 S. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Developments in Mathematics |v 20 | |
| 650 | 4 | |a Semigroups | |
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| 689 | 0 | 0 | |a Halbgruppe |0 (DE-588)4022990-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a García-Sánchez, Pedro A. |e Verfasser |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4419-0160-6 |
| 830 | 0 | |a Developments in Mathematics |v 20 |w (DE-604)BV013103064 |9 20 | |
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Datensatz im Suchindex
| _version_ | 1804140814911143936 |
|---|---|
| adam_text | Contents
Introduction
....................................................... 1
1 Notable
elements
............................................... 5
Introduction
.................................................... 5
1
Monoids and monoid homomorphisms
......................... 5
2
Multiplicity and embedding dimension
........................ 6
3
Frobenius number and genus
................................. 9
4
Pseudo-Frobenius numbers
.................................. 13
Exercises
...................................................... 16
2
Numerical semigroups with maximal embedding dimension
......... 19
Introduction
.................................................... 19
1
Characterizations
........................................... 20
2
Arf numerical semigroups
................................... 23
3
Saturated numerical semigroups
.............................. 28
Exercises
...................................................... 31
3
Irreducible numerical semigroups
................................ 33
Introduction
.................................................... 33
1
Symmetric and pseudo-symmetric numerical semigroups
......... 33
2
Irreducible numerical semigroups with arbitrary multiplicity
and embedding dimension
................................... 38
3
Unitary extensions of a numerical semigroup
................... 44
4
Decomposition of a numerical semigroup into
irreducibles
........ 47
5
Fundamental gaps of a numerical semigroup
.................... 51
Exercises
...................................................... 53
4
Proportionally modular numerical semigroups
.................... 57
Introduction
.................................................... 57
1
Periodic
subadditive
functions
................................ 57
viij
Contents
2
The numerical semigroup associated to an interval
of rational numbers
......................................... 59
3
Bézout
sequences
.......................................... 61
4
Minimal generators of a proportionally modular numerical
semigroup
................................................. 65
5
Modular numerical semigroups
............................... 69
6
Opened modular numerical semigroups
........................ 71
Exercises
...................................................... 75
5
The quotient of a numerical semigroup by a positive integer
........ 77
Introduction
.................................................... 77
1
Notable elements
........................................... 78
2
One half of an irreducible numerical semigroup
................. 79
3
Numerical semigroups having a Toms decomposition
............ 83
Exercises
...................................................... 88
6
Families of numerical semigroups closed under finite
intersections and adjoin of the Frobenius number
.................. 91
Introduction
.................................................... 91
1
The directed graph of the set of numerical semigroups
............ 91
2
Frobenius varieties
......................................... 93
3
Intersecting Frobenius varieties
............................... 98
4
Systems of generators with respect to a Frobenius variety
......... 99
5
The directed graph of a Frobenius variety
......................100
Exercises
......................................................104
7
Presentations of a numerical semigroup
..........................105
Introduction
....................................................105
1
Free monoids and presentations
...............................106
2
Minimal presentations of a numerical semigroup
................110
3
Computing minimal presentations
.............................113
4
An upper bound for the cardinality of a minimal presentation
......117
Exercises
......................................................120
8
The gluing of numerical semigroups
..............................123
Introduction
....................................................123
1
The concept of gluing
.......................................124
2
Complete intersection numerical semigroups
....................127
3
Gluing of numerical semigroups
..............................129
4
Free numerical semigroups
..................................132
Exercises
......................................................135
Contents ix
9
Numerical semigroups with embedding dimension three
............137
Introduction
....................................................137
1
Numerical semigroups with Apery sets of unique expression
......137
2
Irreducible numerical semigroups with embedding
dimension three
............................................141
3
Pseudo-Frobenius numbers and genus of an embedding
dimension three numerical semigroup
.........................147
Exercises
......................................................154
10
The structure of a numerical semigroup
..........................155
Introduction
....................................................155
1
Levin s theorem
............................................155
2
Structure theorem
..........................................159
3
Ot-monoids
................................................162
Exercises
......................................................168
Bibliography
.......................................................171
List of symbols
.....................................................177
Index
.............................................................179
|
| any_adam_object | 1 |
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| ctrlnum | (OCoLC)436030789 (DE-599)DNB995510245 |
| 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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| id | DE-604.BV035844960 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:05:58Z |
| institution | BVB |
| isbn | 9781441901590 |
| language | English |
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| physical | IX, 181 S. 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Developments in Mathematics |
| series2 | Developments in Mathematics |
| spelling | Rosales, José C. Verfasser aut Numerical semigroups by J. C. Rosales ; P. A. García-Sánchez New York, NY [u.a.] Springer 2009 IX, 181 S. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Developments in Mathematics 20 Semigroups Halbgruppe (DE-588)4022990-7 gnd rswk-swf Halbgruppe (DE-588)4022990-7 s DE-604 García-Sánchez, Pedro A. Verfasser aut Erscheint auch als Online-Ausgabe 978-1-4419-0160-6 Developments in Mathematics 20 (DE-604)BV013103064 20 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018703178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rosales, José C. García-Sánchez, Pedro A. Numerical semigroups Developments in Mathematics Semigroups Halbgruppe (DE-588)4022990-7 gnd |
| subject_GND | (DE-588)4022990-7 |
| title | Numerical semigroups |
| title_auth | Numerical semigroups |
| title_exact_search | Numerical semigroups |
| title_full | Numerical semigroups by J. C. Rosales ; P. A. García-Sánchez |
| title_fullStr | Numerical semigroups by J. C. Rosales ; P. A. García-Sánchez |
| title_full_unstemmed | Numerical semigroups by J. C. Rosales ; P. A. García-Sánchez |
| title_short | Numerical semigroups |
| title_sort | numerical semigroups |
| topic | Semigroups Halbgruppe (DE-588)4022990-7 gnd |
| topic_facet | Semigroups Halbgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018703178&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013103064 |
| work_keys_str_mv | AT rosalesjosec numericalsemigroups AT garciasanchezpedroa numericalsemigroups |