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
$R^n$,

$R$
 the basering, generated by vectors
$v_1, \ldots, v_k$, then $v_1, \ldots, v_k$
may be considered as the generators of relations of
$R^n/M$
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$\times$k
 for
R$^n$/M,
i.e., the columns of A are the vectors
$v_1, \ldots, v_k$
which generate M (cf. Representation of mathematical objects).

* module declarations::
* module expressions::
* module operations::
* module related functions::

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
</font>

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