Module (mathematics): Difference between revisions

Revision as of 10:43, 8 May 2022

Revision as of 10:48, 3 August 2022

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{{Ring theory sidebar}}

{{Algebraic structures|module}}

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

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.