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What (who) is interchangeable module - definition

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

Module (mathematics)

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.

https://en.wikipedia.org/wiki/Module_(mathematics)

Dualizing module

Canonical module; Dualising 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.

https://en.wikipedia.org/wiki/Dualizing_module

Differential graded module

Z-GRADED MODULE WITH A COMPATIBLE DIFFERENTIAL

Draft:Differential graded module; Dg-module; Dg module; DG-module; DG module

In algebra, a differential graded module, or dg-module, is a \mathbb{Z}-graded module together with a differential; i.e.

https://en.wikipedia.org/wiki/Differential_graded_module

Wikipedia

Module (mathematics)

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.

Like a vector space, a module is an additive abelian group, and scalar multiplication is distributive over the operation of addition between elements of the ring or module and is compatible with the ring multiplication.

Modules are very closely related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are used widely in algebraic geometry and algebraic topology.

https://en.wikipedia.org/wiki/Module (mathematics)