Abstract
For a numerical semigroup S , a positive integer a and a nonzero element m of S , we define a new numerical semigroup R ( S , a , m ) and call it the ( a , m )-rotation of S . In this paper we study the Frobenius number and the singularity degree of R ( S , a , m ). Moreover, we observe that the rotations of ℕ are precisely the modular numerical semigroups.
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