41.19 Module Homomorphism Records

Module homomorphism records have at least the following components.

isGeneralMapping :

true,

isMapping :

true,

isHomomorphism:

true,

domain :

Mappings,

source :

the source of the homomorphism, a module M_1,

range :

the range of the homomorphism, a module M_2,

preImage :

the module M_1,

basisImage :

a vector space basis of the image of M_1,

preimagesBasis :

a list of preimages of the basis vectors in basisImage

operations :

the operations record of the homomorphism.

If the source is a (factor of a) free module then there are also the components

genimages :

a list of images of the generators of the source,

alghom :

the underlying algebra homomorphism from the ring acting on M_1 to the ring acting on M_2.

If the source is a (factor of a) row module then there are also the components

basisSource :

a vector space basis of M_1,

imagesBasis :

a list of images of the basis vectors in basisSource.

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