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ON ARF CLOSURE OF SOME SYMMETRIC NUMERICAL SEMIGROUPS WITH MULTIPLICITY $p$-PRIME
Keywords:
determine number, symmetric numerical semigroups, Arf closure, gaps.DOI:
https://doi.org/10.17654/0972555523024Abstract
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, 2023
Revised: August 1, 2023
Accepted: September 12, 2023
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