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

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