Solitons: Differential equations, symmetries, and infinite-dimensional algebras
《Solitons: Differential equations, symmetries, and infinite-dimensional algebras》 · 第 564 页 · Definition B.39
An $A$-module $M$ is called $\mathfrak a$-adically complete if the canonical homomorphism $M\to\widehat M$ is an isomorphism. In particular, $A$ is said to be $\mathfrak a$-adically complete if the canonical homomorphism $A\to\varprojlim_n A/\mathfrak a^nA$ is an isomorphism. If $A$ is a local ring, we usually endow $A$ with the $\mathfrak m$-adic topology, where $\mathfrak m$ is the maximal ideal of $A$. If $A$ is $\mathfrak m$-adically complete, we simply say that $A$ is complete.