The Schur group of a commutative ring, R , with identity consists of all classes in the Brauer group of R which contain a homomorphic image of a group ring R G for some finite group G . It is the purpose of this article to continue an investigation of this group which was introduced in earlier work as a natural generalization of the Schur group of a field. We generalize certain facts pertaining to the latter, among which are results on extensions of automorphisms and decomposition of central simple algebras into a product of cyclics. Finally we introduce the Schur exponent of a ring which equals the well-known Schur index in the global or local field case.