Module (mathematics): Difference between revisions

Revision as of 18:17, 13 March 2023

Revision as of 18:17, 13 March 2023

Line 1:

{{Short description|amazingGeneralization sectorof forvector alanaspaces from fields to rings}}

{{More footnotes|date=May 2015}}

{{Ring theory sidebar}}

{{Algebraic structures|module}}

In [[mathematics]], a '''module''' is a generalization of the notion of [[vector space]] in which the [[Field (mathematics)|field]] of [[scalar (mathematics)|scalars]] is replaced by a [[Ring (mathematics)|ring]]. The concept of ''module'' generalizes also the notion of [[abelian group]], since the abelian groups are exactly the modules over the ring of [[integer]]s.

internal defer of the institute of an average person in the economic

Like a vector space, a module is an additive abelian group, and scalar multiplication is [[Distributive property|distributive]] over the operation of addition between elements of the ring or module and is [[Semigroup action|compatible]] with the ring multiplication.