Change of rings

In algebra, given a ring homomorphism f : R → S {displaystyle f:R o S} , there are three ways to change the coefficient ring of a module; namely, for a right R-module M and a right S-module N, In algebra, given a ring homomorphism f : R → S {displaystyle f:R o S} , there are three ways to change the coefficient ring of a module; namely, for a right R-module M and a right S-module N, They are related as adjoint functors: