Discrete norm

From Encyclopedia of Mathematics
Jump to: navigation, search

A norm on a skew-field the group of values of which is isomorphic to the group of integers $ \mathbf Z $. In such a case the ring is a discretely-normed ring. A discrete norm, more exactly, a discrete norm of height (or rank) $ r $ is also sometimes understood as the norm having as group of values the $ r $- th direct power of the group $ \mathbf Z $ with the lexicographical order.


This notion is more commonly called a discrete valuation. A discretely-normed ring is usually called a discrete valuation domain. See also Norm on a field; Valuation.


[a1] O. Endler, "Valuation theory" , Springer (1972)
How to Cite This Entry:
Discrete norm. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.I. Danilov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article