Numerical Semigroups and Applications

Abdallah Assi graduated in Mathematics at the University Joseph Fourier (Grenoble, France). He obtained his Ph.D. in Mathematics at the same university and his HDR-Habilitation à diriger les recherches- at the University of Angers (France). He has a parmanent position at the Department of Mathematics in the University of Angers since 1995. His research interests are in affine geometry, numerical semigroups, and the theory of singularities.Pedro A. Garcia-Sanchez was born in Granada, Spain, in 1969. Since 1992 he teaches in the Departmento de Algebra at the Universidad de Granada. He graduated in Mathematics and in Computer Science (Diploma) in 1992. He defended his PhD Thesis "Affine semigroups" in 1996, and since 1999 he has a permanent position at the Universidad de Granada. His main research interests are numerical semigroups, commutative monoids and nonunique factorization invariants.

• 1 Numerical semigroups, the basics.- 2 Irreducible numerical semigroups.- 3 Semigroup of an irreducible meromorphic series.- 4 Minimal presentations.- 5 Factorizations and divisibility.

“This book gives some basic notions related to numerical semigroups, and presents applications of numerical semigroups in algebraic geometry, number theory and coding theory. … The book contains numerous examples and computational experiments. … This book will be of value for undergraduate students and also for researchers interested in numerical semigroups and their applications.” (Attila Nagy, Mathematical Reviews, May, 2017)​