Changing Rings

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

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): AlgMatV, Rng, Map -> AlgMat, Map

Given a matrix algebra \(A\) with base ring \(R\), together with a ring \(S\) and a homomorphism \(f: R \rightarrow S\), 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 \(B\).

hom< A -> B | f >: AlgMat, AlgMat, Map -> Map

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.