Given one or more existing modules, various standard constructions are available to construct new modules.
Given a module M with base ring R, together with a ring S, construct the module N with base ring S obtained by coercing the components of elements of M into N, together with the homomorphism from M to N.
Given a module M with base ring R, together with a ring S, and a homomorphism f: R -> S, construct the module N with base ring S obtained by mapping the components of elements of M into N by f, together with the homomorphism from M to N.
Change the coefficient ring of x to be R.
Given R-modules M and N, construct the direct sum D of M and N as an R-module. The embedding maps from M into D and from N into D respectively, and the projection maps from D onto M and from D onto N respectively are also returned.
Given a sequence Q of R-modules, construct the direct sum D of these modules. The embedding maps from each of the elements of Q into D and the projection maps from D onto each of the elements of Q are also returned.