Is there a name for a local homomorphism $\varphi:A\longrightarrow B$ of local rings $A$ and $B$, whose completion $\hat{\varphi}:\hat{A}\longrightarrow\hat{B}$ is a finite homomorphism? (that is, $\hat{B}$ is a module finite extension of $\hat{A}$ via $\hat{\varphi}$). Perhaps *formally finite*?

**EDIT**: Assume $A$ and $B$ are Noetherian.

analytically finite? Google does not show any thing like that though. – Hailong Dao Aug 1 '11 at 0:50analytically finite, if there is no name for this. – Mahdi Majidi-Zolbanin Aug 1 '11 at 19:03quasi-finite(see pages 1 and 2 of SGA 1). – Mahdi Majidi-Zolbanin Aug 4 '11 at 15:31