Given one or more existing modules, various standard constructions are available to construct new modules.
Given an A-module M with base ring R, together with a ring S, such that there is a natural homomorphism from R to S, construct the module N with base ring S where N is obtained from M by coercing the components of the vectors of M into N. The corresponding homomorphism from M to N is returned as a second value.
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, where N is obtained from M by applying f to the components of the vectors of M. The corresponding homomorphism from M to N is returned as a second value.
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.
Given a K[G]-module M of dimension n over the field K, and a nonsingular n x n matrix T over K, construct the K[G]-module N which corresponds to taking the rows of T as a basis for M.[Next][Prev] [Right] [Left] [Up] [Index] [Root]