The aim of this work is to exhibit the relationship between the Arf closure of a numerical semigroup$S$ and its Lipman semigroup $L(S).$ This relationship is then used to give direct proofs of some characterizations of Arf numerical semigroups through their Lipman sequences of semigroups. We also give an algorithmic construction of the Arf closure of a numerical semigroup via its Lipman sequence of semigroups.
Numerical semigroups, Arf numerical semigroups, Arf closure
İLHAN, SEDAT and KARAKAŞ, HALİL İBRAHİM
"Arf numerical semigroups,"
Turkish Journal of Mathematics: Vol. 41:
6, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss6/7