Holdings: Numerical semigroups

Numerical semigroups:

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Bibliographic Details
Main Authors:	Rosales, José C. (Author), García-Sánchez, Pedro A. (Author)
Format:	Book
Language:	English
Published:	New York, NY [u.a.] Springer 2009
Series:	Developments in Mathematics 20
Subjects:	Semigroups Halbgruppe
Online Access:	Inhaltsverzeichnis
Physical Description:	IX, 181 S. 235 mm x 155 mm
ISBN:	9781441901590

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MARC


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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
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author	Rosales, José C. García-Sánchez, Pedro A.
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indexdate	2024-07-09T22:05:58Z
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isbn	9781441901590
language	English
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physical	IX, 181 S. 235 mm x 155 mm
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series	Developments in Mathematics
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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
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