Let R be a ring. An R-module (or, more exactly, an R-right module) is an additive abelian group on that R acts from the right.
A module is of interest mainly as operation domain of an algebra (see chapter Algebras). Thus it is the natural place to store information about the operation of the algebra, for example whether it is irreducible. But since a module is a domain it has also properties of its own, independent of the algebra.
According to the different types of algebras in GAP, namely matrix algebras and finitely presented algebras, at the moment two types of modules are supported in GAP, namely row modules and their quotients for matrix algebras and free modules and their submodules and quotients for finitely presented algebras. See Row Modules and Free Modules for more information.
For modules, the same concept of parent and substructures holds as for row spaces. That is, a module is stored either as a submodule of a module, or it is not (see Submodule, AsSubmodule for the details).
Also the concept of factor structures and cosets is the same as that for row spaces (see Quotient Spaces, Row Space Cosets), especially the questions about a factor module is mainly delegated to the numerator and the denominator, see also Operations for Row Modules.
GAP 3.4.4