Download Absolute Values

Queue processing for download document Let K be a field. An absolute value v on K is a real-valued function x ↦ |x| v on K satisfying the following three properties: AV 1 We have |x| v ≧ 0 for all x ∊ K, and |x| v = 0 if and only if x = 0.  AV 2 For all x, y ∊ K, we have |xy| v = |x| v |y| v .