Picard group of a ringoid

Tensor product gives a monoid structure on the class of isomorphism types of R,R-bimodules, for a ring or ringoid R. Restricting to those elements for which there is a two-sided inverse yields a group. I am inclined to call this the nonabelian Picard group and denote it by NPic(R). If we start with a commutative ring R, then the usual Picard group of R, Pic(R), can be viewed as an abelian subgroup of NPic(R). Has anyone seen this before? Does anyone have some other idea about what this should be called? Bill Rowan