Singular Manual: module (plural)

> | ### 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.
> 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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