
7.2.3 module (plural)
Modules are left submodules of a free module over the basering with basis
gen(1) , gen(2) , ..., gen(n) for some natural number n .
They are represented by lists of vectors, which generate the left submodule.
Like vectors, they can only be defined or accessed with respect to a basering.
If
is a left submodule of
(where
is the basering) generated by vectors
, then these generators may be considered as the generators of relations of
between the canonical generators gen(1) ,...,gen(n) .
Hence, any finitely generated
module can be represented in PLURAL
by its module of relations. This is the socalled Cokerrepresentation.
The assignments module M=v1,...,vk; matrix A=M;
create the presentation matrix of size
,with the columns of A being the vectors
which generate .
