Revision as of 12:48, 3 May 2022 edit TakuyaMurata (talk \| contribs) Extended confirmed users, IP block exemptions, Pending changes reviewers 92,676 edits →Types of modules: {{see also\|Glossary of module theory}} ← Previous edit		Revision as of 10:43, 8 May 2022 edit undo Athel cb (talk \| contribs) Extended confirmed users, IP block exemptions 22,033 edits one → notion (almost intelligible before) Next edit →
Line 3: {{Ring theory sidebar}} {{Algebraic structures\|module}} In [[mathematics]], a '''module''' is a generalization of the notion of [[vector space]], wherein 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 ~~one~~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.

Module (mathematics): Difference between revisions