ON THE TYPE SEQUENCES OF SOME ONE DIMENSIONAL RINGS

Abstract. In this article in Section 2 we describe the holes and their positions of a numerical semigroup and use this description to compute the type sequence of the semigroup generated by an arithmetic sequence m0,m1,...,mp+1 explicitly (see 3.8 and 3.9). Introduction. Let (R,mR) be a noetherian local one dimensional analyt-ically irreducible domain, i.e., the m-adic completion R ̂ of R is a domain or, equivalently, the integral closure R of R in its quotient field Q(R) is a discrete valuation ring and a finite R-module. We further assume that R is residually rational, i.e., R and R have the same residue field. A particular importan