Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 570 页 · Proposition B.71
Let $A$ be a ring which is not a field. Then $A$ is called a discrete valuation ring if it satisfies the following equivalent properties: (i) $A$ is a local principal ideal domain; (ii) $A$ is a local one-dimensional integrally closed noetherian ring; (iii) $A$ is a noetherian valuation ring.