Original sentence: Algebraic number fields K come with a canonical norm function on them: the field norm N that takes an algebraic element α to the product of all the conjugates of α.If N satisfies the axioms of a Euclidean function then the number field K is called norm-Euclidean.This norm maps the ring of integers of a number field K, say OK, to the rational integers, so is a candidate to be a Euclidean norm on this ring
Edited sentence: Algebraic number fields K come with a canonical norm function on them: the absolute value of the field norm N that takes an algebraic element α to the product of all the conjugates of α.If this norm satisfies the axioms of a Euclidean function then the number field K is called norm-Euclidean.This norm maps the ring of integers of a number field K, say OK, to the rational integers, so it is a candidate to be a Euclidean norm on this ring