Notable elements

Abstract

The study of numerical semigroups is equivalent to that of nonnegative integer solutions to a linear nonhomogeneous equation with positive integer coefficients. Thus it is a classic problem that has been widely treated in the literature (see [12, 13, 22, 28, 42, 101, 102]). Following this classic line, two invariants play a role of special relevance in a numerical semigroup. These are the Frobenius number and the genus. Besides, in the literature one finds many manuscripts devoted to the study of analytically unramified one-dimensional local domains via their value semigroups, which turn out to be numerical semigroups (just to mention some of them, see [5, 6, 19, 27, 32, 44, 105, 107]). Playing along this direction other invariants of a numerical semigroup arise: the multiplicity, embedding dimension, degree of singularity, conductor, Apéry sets, pseudo-Frobenius numbers and type. These invariants have their interpretation in this context, and this is the reason why their names may seem bizarre in the scope of monoids. In this sense the monograph [5] serves as an extraordinary dictionary between these apparently two different parts of Mathematics.