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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.
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.
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Wed Apr 24 15:09:57 EST 2013