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Numerical Semigroups

:	J.C. Rosales, P. A. García-Sánchez
:	Numerical Semigroups
:	Springer-Verlag
:	9781441901606
:	1
:	CHF 85.40
:

:	Arithmetik, Algebra
:	English

:	181
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

'Numerical Semigroups' is the first monograph devoted exclusively to the development of the theory of numerical semigroups. This concise, self-contained text is accessible to first year graduate students, giving the full background needed for readers unfamiliar with the topic. Researchers will find the tools presented useful in producing examples and counterexamples in other fields such as algebraic geometry, number theory, and linear programming.

	Contents	7
	Introduction	10
	Notable elements	13
	Introduction	13
	Monoids and monoid homomorphisms	13
	Multiplicity and embedding dimension	14
	Frobenius number and genus	17
	Pseudo-Frobenius numbers	21
	Exercises	24
	Numerical semigroups with maximal embedding dimension	27
	Introduction	27
	Characterizations	28
	Arf numerical semigroups	31
	Saturated numerical semigroups	36
	Exercises	39
	Irreducible numerical semigroups	41
	Introduction	41
	Symmetric and pseudo-symmetric numerical semigroups	41
	Irreducible numerical semigroups with arbitrary multiplicity and embedding dimension	46
	Unitary extensions of a numerical semigroup	52
	Decomposition of a numerical semigroup into irreducibles	55
	Fundamental gaps of a numerical semigroup	59
	Exercises	61
	Proportionally modular numerical semigroups	64
	Introduction	64
	Periodic subadditive functions	64
	The numerical semigroup associated to an intervalof rational numbers	66
	Bézout sequences	68
	Minimal generators of a proportionally modular numerical semigroup	72
	Modular numerical semigroups	76
	Opened modular numerical semigroups	78
	Exercises	82
	The quotient of a numerical semigroup by a positive integer	84
	Introduction	84
	Notable elements	85
	One half of an irreducible numerical semigroup	86
	Numerical semigroups having a Toms decomposition	90
	Exercises	95
	Families of numerical semigroups closed under finite intersections and adjoin of the Frobenius number	98
	Introduction	98
	The directed graph of the set of numerical semigroups	98
	Frobenius varieties	100
	Intersecting Frobenius varieties	105
	Systems of generators with respect to a Frobenius variety	106
	The directed graph of a Frobenius variety	107
	Exercises	111
	Presentations of a numerical semigroup	112
	Introduction	112
	Free monoids and presentations	113
	Minimal presentations of a numerical semigroup	117
	Computing minimal presentations	120
	An upper bound for the cardinality of a minimal presentation	124
	Exercises	127
	The gluing of numerical semigroups	130
	Introduction	130
	The concept of gluing	131
	Complete intersection numerical semigroups	134
	Gluing of numerical semigroups	136
	Free numerical semigroups	139
	Exercises	142
	Numerical semigroups with embedding dimension three	144
	Introduction	144
	Numerical semigroups with Apéry sets of unique expression	144
	Irreducible numerical semigroups with embedding dimension three	148
	Pseudo-Frobenius numbers and genus of an embedding dimension three numerical semigroup	154
	Exercises	161
	The structure of a numerical semigroup	162
	Introduction	162
	Levin's theorem	162
	Structure theorem	166
	N-monoids	169
	Exercises	175
	Bibliography	177
	List of symbols	182
	Index	184