Formally smooth bimodules

Abstract

The notion of a formally smooth bimodule is introduced and its basic properties are analyzed. In particular it is proven that a $B$-$A$ bimodule $M$ which is a generator left $B$-module is formally smooth if and only if the $M$-Hochschild dimension of $B$ is at most one. It is also shown that modules $M$ which are generators in the category $\sigma[M]$ of $M$-subgenerated modules provide natural examples of formally smooth bimodules.