Meaning of discrete valuation | Babel Free

Definitions

A valuation (on some field) that takes integer values (including infinity).

Examples

“Therefore the theory branches in two essential parts : first the study⟳ of discrete valuations of the Weyl field D#95;1(K) extending a discrete valuation of K, secondly the discrete valuations of D#95;1(K) having the purely transcendental field K(t) as a residue field.”

“One of the few possibilities to extend⟳ some arithmetic aspects of number⟳ theory to more abstract fields is via valuation theory and, as a first step, we may restrict attention to discrete valuations.”

“Let⟳ k be a field with a nontrivial discrete valuation which is complete⟳ and has perfect residue field.”

CEFR level