(a) If ∫ is a right ideal of a ring R with identity and Ba left R-module, then there is a group isomorphism R/ I⊗_R B ≅ B/ IB, where IB is the subgroup of B generated by all elements rb with r ϵ I, b ϵ B.

(b) If R is commutative and I,J are ideals of R, then there is an R-module isomorphism R/l⊗_R R/J ≅ R/(I + J).