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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
13#13 is a left submodule of
90#90(where
53#53 is the basering) generated by vectors
91#91, then these generators may be considered as the generators of relations of
92#92between the canonical generators gen(1),...,gen(n).
Hence, any finitely generated
53#53-module can be represented in PLURAL
by its module of relations. This is the so-called Coker-representation.
The assignments module M=v1,...,vk; matrix A=M;
create the presentation matrix of size
193#193,with the columns of A being the vectors
91#91 which generate 13#13.
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