Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 570 页 · Definition/Proposition B.69
Let $K$ be a field and let $A$ be a subring of $K$. The ring $A$ is called a valuation ring of $K$ if it satisfies the following equivalent properties. (i) For every $a\in K^\times$ one has $a\in A$ or $a^{-1}\in A$.