Standard Constructions

Given one or more existing modules, various standard constructions are available to construct new modules.

Changing the Coefficient Ring

ChangeRing(M, S) : ModRng, Rng -> ModRng, Map

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.

ChangeRing(M, S, f) : ModRng, Rng, Map -> ModRng, Map

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.

ChangeUniverse(~x, R) : ModTupRngElt, Rng -> ModRng, Map

Change the coefficient ring of x to be R.

Direct Sums

DirectSum(M, N) : ModRng, ModRng -> ModRng, Map, Map, Map, Map

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.

DirectSum(Q) : [ ModRng ] -> [ ModRng ], [ Map ], [ Map ]

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.