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m Fixed typo Tags: Mobile edit Mobile app edit iOS app edit App select source |
Changed the incorrect claim that a module "generalizes" an abelian group. Hopefully not a controversial change as this was talked about extensively on the talk page. Tag: Reverted |
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{{Ring theory sidebar}}
{{Algebraic structures|module}}
In [[mathematics]], a '''module''' is a generalization of the notion of a [[vector space]] in which the [[Field (mathematics)|field]] of [[scalar (mathematics)|scalars]] is replaced by a (not necessarily [[Commutative_ring|commutative]]) [[Ring (mathematics)|ring]].
Like a vector space, a module is an additive abelian group, and scalar multiplication is [[Distributive property|distributive]] over the operations of addition between elements of the ring or module and is [[Semigroup action|compatible]] with the ring multiplication.
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