ON ARF CLOSURE OF SOME SYMMETRIC NUMERICAL SEMIGROUPS WITH MULTIPLICITY -PRIME

Abstract

This work is about symmetric numerical semigroups. The symmetric numerical semigroups are very important in semigroup theory. They play an important role especially in algebraic geometry, coding theory and other areas of algebra. Here, we examine Arf closure of $S_q$ symmetric numerical semigroup, and give some relations between $S_q$ and Arf closure $S_q$ such that $S_q=\langle p, p q+k\rangle$, where $p$ is a prime number and $q \geq 1, q \in \mathbb{Z}$ for $k=1,2$ and $p-1$. Received: June 15, 2023Revised: August 1, 2023Accepted: September 12, 2023