Gauss' Lemma for function fields

Abstract

Let L be a number field and OL the ring of algebraic integers in L. For a polynomial f with coefficients in OL, the content of f in L is the ideal of OL generated by coefficients of f. The polynomial f is primitive in L if the content of f in L is OL. In 2005, Arturo Magidin and David McKinnon proved the Gauss’ lemma for number fields, the product of two primitive polynomials is also primitive, and some applications following from Gauss’ lemma for number fields. A function field K over a finite field k is a finite separable field extension over k(x) where x is a transcendantal element. In this research, we study Magidin and McKinnon’s work on the function fields.