on a Euclidean domain D influence the arithmetic structure of D in any way? Explain. Theory 15. Let D be a Euclidean domain and let v be a Euclidean norm on D. Show that if a and b are associates in...

Section 46 number 15

Extracted text: on a Euclidean domain D influence the arithmetic structure of D in any way? Explain. Theory 15. Let D be a Euclidean domain and let v be a Euclidean norm on D. Show that if a and b are associates in D, then v(a) = v(b). Fuglidean norm on D Show that for nonzero a, b e D, one has