Given a matrix algebra A with base ring R, together with a ring S, construct the matrix algebra B with base ring S obtained by coercing the components of elements of A into S, together with the homomorphism from A to B.

ChangeRing(A, S, f) : AlgMat, Rng, Map -> AlgMat, Map

Given a matrix algebra A with base ring R, together with a ring S and a homomorphism f: R -> S, construct the matrix algebra B with base ring S obtained by mapping the components of elements of R into S by f, together with the homomorphism from A to B.

Given full matrix algebras A and B, together with a homomorphism f from the base ring R of A to the base ring S of B, create the homomorphism from A to B which, given a matrix in A, applies f to the entries of the matrix.