Discrete rings
An absolute value on a field \(F\) is a function \(\varphi: F\to \mathbb{R}^\geq\) which is either a Krull valuation or the restriction of (some power of) the usual absolute value of \(\mathbb{C}\) to a subfield. An absolute value defines a topology on the field \(F\), hence, by restriction, also on every subring (unitary or not). The author studies subrings that are discrete, notably for the cases that \(F\) is the completion of a function field \(K(X)\) in one variable with respect to the \((1/X)\)-adic topology, or that \(F\) is \(\mathbb{R}\) or \(\mathbb{C}\) with the usual absolute value.
scientific article; zbMATH DE number 920035