Perfect numerical semigroups

In this thesis, perfect numerical semigroups, which are a subclass of numerical semigroups, are discussed. Some results have been obtained, such as that a numerical semigroup is a perfect numerical semigroup if it does not contain an isolated gap, and that all submonoids of perfect numerical semigroups are perfect. In the first chapter, various definitions and theorems that form the basis of numerical semigroups are mentioned. Then. The conditions under which numerical semigroups become perfect numerical semigroups are explained. In particular, the structures of perfect numerical semigroups and various theorems on these semigroups are discussed. By using perfect numerical semigroups, ratios are given in perfect numerical semigroups with embedding dimension 3, and various theorems and results have emerged in these perfect numerical semigroups. Keywords: Numerical semigroups, Perfect numerical semigroups, Frobenius number, Isolated gaps, Genus, Embedding dimension