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Standard Constructions

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

Subsections

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.
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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013