paper

Formally smooth bimodules

arXiv:math/0701473 · doi:10.1017/is007011015jkt012

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 $I ¨ [M]$ of $M$ -subgenerated modules provide natural examples of formally smooth bimodules.

17 pages