Projective modules over pullback rings

Given two homomorphisms of rings j1:R1 → R' and j2: R2 → R' we may construct a new ring R called the pullback of R1 and R2 over R', together with homomorphisms i1:R →R1 and i2:R→R2 such that j1i1= j2i2. There are many instances where special cases of pullbacks have been studied, either to construct new examples of rings or to reduce various problems to those concerning much simpler rings. A few of these instances are given in the references. Thus a general study of the properties of pullbacks in terms of those of the component rings would seem to be useful.