Factorization in K[[S]]
David F. Anderson, Janice Winner · 2017
Let K be a field, S = 〈 n 1 ,…, n r 〉 a numerical semigroup, and K [[ S ]] the (power series) semigroup ring. In this paper, we study lengths of factorizations in K [[ S ]]. We show that n r / n 1 ≤ ρ ( K [[ S ]]) ≤ ( g ( S ) + n 1 )/ n 1 , where g ( S ) is the Frobenius number of S . This inequality is an equality when g ( S ) + n 1 = n r , but in general ρ ( K [[ S ]]) may lie strictly between the two bounds.