Formally smooth bimodules

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