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4.10 module
Modules are submodules of a free module over the basering with basis
gen(1) , gen(2) , … .
They are represented by lists of vectors which generate the submodule.
Like vectors they
can only be defined or accessed with respect to a basering.
If
M
is a submodule of
Rn,
R
the basering, generated by vectors
v1,…,vk, then v1,…,vk
may be considered as the generators of relations of
Rn∕M
between the canonical generators gen(1) ,…,gen(n) .
Hence any finitely generated
R
-module can be represented in SINGULAR
by its module of relations. The assignments
module M=v1,...,vk; matrix A=M;
create the presentation matrix of size
n×k
for
Rn/M,
i.e., the columns of A are the vectors
v1,…,vk
which generate M (cf. Representation of mathematical objects).
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