Discrete norm

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.

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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.

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