A module over a ring is an abelian group with a distributive, unital -action, that is, a vector-space whose scalars live in a ring rather than a field. Equivalently it is a ring homomorphism, the action-equals-homomorphism pattern shared by a group action and a representation , so a module is a representation of . In the same vein a quiver representation is a module over the path algebra of the quiver. Over a field every module is free, meaning it has a basis, whereas over a general ring most are not, since over is all torsion.