Module (mathematics): Difference between revisions

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m typo of "where in"
Undid good faith revision 1102102031 by Concinnitas43 (talk). "Wherein" is an English word and is what was intended. But I've replaced it by "in which", which is more common language.
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{{Ring theory sidebar}}
{{Algebraic structures|module}}
In [[mathematics]], a '''module''' is a generalization of the notion of [[vector space]], where in which the [[Field (mathematics)|field]] of [[scalar (mathematics)|scalars]] is replaced by a [[Ring (mathematics)|ring]]. The concept of ''module'' isgeneralizes 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.