### 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 so-called Coker-representation.
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 .

> 7.2.3.1 module declarations (plural) |  |
> 7.2.3.2 module expressions (plural) |  |
> 7.2.3.3 module operations (plural) |  |
> 7.2.3.4 module related functions (plural) |  |

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