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.
|[a1]||O. Endler, "Valuation theory" , Springer (1972)|
Discrete norm. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Discrete_norm&oldid=46734