Kfagerstrom: Created page with "Let $R$ be a ring with $1\neq0$ . A ''Left'' $R$ -mod is an abelian group $(M,+)$ together with an action of $R$ on
2023-03-08T22:07:12Z

Created page with "Let <math>R</math> be a ring with <math>1\neq0</math>. A ''Left'' <math>R</math>-mod is an abelian group <math>(M,+)</math> together with an action of <math>R</math> on <mat..."

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Let <math>R</math> be a ring with <math>1\neq0</math>.

A ''Left'' <math>R</math>-mod is an abelian group <math>(M,+)</math> together with an action of <math>R</math> on <math>M</math>, <math>R\times M \to M</math>, such that for all <math>r,s\in R</math>, <math>m,n\in M</math>:

* <math>(r+s)m=rm+sm</math>
* <math>(rs)m=r(sm)</math>
* <math>r(m+n)=rm+rn</math>
* <math>1\cdot m=m</math>

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