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What (who) is G-module - definition
G-module
![The [[torus]] can be made an abelian group isomorphic to the product of the [[circle group]]. This abelian group is a [[Klein four-group]]-module, where the group acts by reflection in each of the coordinate directions (here depicted by red and blue arrows intersecting at the identity element).](https://commons.wikimedia.org/wiki/Special:FilePath/Toroidal coord.png?width=200 "The [[torus]] can be made an abelian group isomorphic to the product of the [[circle group]]. This abelian group is a [[Klein four-group]]-module, where the group acts by reflection in each of the coordinate directions (here depicted by red and blue arrows intersecting at the identity element).")
AN ABELIAN GROUP
ZG-module; Draft:ZG-module
In mathematics, given a group G, a G-module is an abelian group M on which G acts compatibly with the abelian group structure on M. This widely applicable notion generalizes that of a representation of G.
Module (mathematics)
GENERALIZATION OF VECTOR SPACE, WITH SCALARS IN A RING INSTEAD OF A FIELD
Module (algebra); Submodule; Module theory; Submodules; R-module; Module over a ring; Left module; Module Theory; Unital module; Module (ring theory); Right module; Left-module; Module mathematics; Ring action; Z-module; ℤ-module
In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring. The concept of module generalizes also the notion of abelian group, since the abelian groups are exactly the modules over the ring of integers.
Dualizing module
In abstract algebra, a dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle of a smooth variety. It is used in Grothendieck local duality.
