Arf halkaları

ABSTRACT ON ARF RINGS Sefa Feza Arslan M.S. in Mathematics Advisor: Asst. Prof. Dr. Sinan Sertöz September, 1994 In this thesis, we worked with curves which have cusp type singularities. We described the Arf theory, which solves the problem of understanding and finding the multiplicity sequence of a curve branch algebraically. We proposed an algorithm for finding the Arf characters of a given curve branch. We also faced the problem of Frobenius, and proposed an algorithm for the solution of problem of Frobenius in the most general case. Keywords : Curve branch, singularity, blow up, multiplicity sequence, Arf ring, Arf semigroup, Arf closure, Arf characters, Frobenius. in