## 4.14 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 is the basering, and is a submodule of

generated by vectors , then

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 SINGULAR by its module of relations. The assignments `module M=v1,...,vk; matrix A=M;` create the presentation matrix of size n k for , i.e., the columns of A are the vectors which generate M (cf. Representation of mathematical objects).

> 4.14.1 module declarations |  |
> 4.14.2 module expressions |  |
> 4.14.3 module operations |  |
> 4.14.4 module related functions |  |

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