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Full-Text Articles in Physical Sciences and Mathematics
Arf Numerical Semigroups, Sedat İlhan, Hali̇l İbrahi̇m Karakaş
Arf Numerical Semigroups, Sedat İlhan, Hali̇l İbrahi̇m Karakaş
Turkish Journal of Mathematics
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.
On A Family Of Saturated Numerical Semigroups With Multiplicity Four, Meral Süer, Sedat İlhan
On A Family Of Saturated Numerical Semigroups With Multiplicity Four, Meral Süer, Sedat İlhan
Turkish Journal of Mathematics
In this study, we will give some results on Arf numerical semigroups of multiplicity four generated by $\left\{ 4,k,k+1,k+2\right\} $ where $k$ is an integer not less than $5$ and $k\equiv 1(\mbox{mod } 4)$.