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Revision as of 22:07, 8 March 2023 by Kfagerstrom (talk | contribs) (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...")
Let \(R\) be a ring with \(1\neq0\).
A Left \(R\)-mod is an abelian group \((M,+)\) together with an action of \(R\) on \(M\), \(R\times M \to M\), such that for all \(r,s\in R\), \(m,n\in M\):
- \((r+s)m=rm+sm\)
- \((rs)m=r(sm)\)
- \(r(m+n)=rm+rn\)
- \(1\cdot m=m\)
