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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 $M$ is a left submodule of $R^n$(where $R$ is the basering) generated by vectors $v_1, \ldots, v_k$, then these generators 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 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 $n \times k$,with the columns of A being the vectors $v_1, \ldots, v_k$ which generate $M$. module declarations (plural) module expressions (plural) module operations (plural) module related functions (plural)