It is proven that every flat connection or covariant derivative ∇ on a left A-module M (with respect to the universal differential calculus) induces a right A-module structure on M so that ∇ is a bimodule connection on M or M is a flat differentiable bimodule. Similarly a flat hom-connection on a right A-module M induces a compatible left A-action.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-2, author = {Tomasz Brzezi\'nski}, title = {A note on flat noncommutative connections}, journal = {Banach Center Publications}, volume = {97}, year = {2012}, pages = {43-53}, zbl = {1272.58004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-2} }
Tomasz Brzeziński. A note on flat noncommutative connections. Banach Center Publications, Tome 97 (2012) pp. 43-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc98-0-2/