Page "Euclidean domain" Paragraph 16

Many authors use other terms such as " degree function ", " valuation function ", " gauge function " or " norm function ", in place of " Euclidean function ".

Some authors also require the domain of the Euclidean function be the entire ring R ; this can always be accommodated by adding 1 to the values at all nonzero elements, and defining the function to be 0 at the zero element of R, but the result is somewhat awkward in the case of K. The definition is sometimes generalized by allowing the Euclidean function to take its values in any well-ordered set ; this weakening does not affect the most important implications of the Euclidean property.