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From Queer Beagle Wiki

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 \(r,s\in R\), \(m,n\in M\):

  • \((r+s)m=rm+sm\)
  • \((rs)m=r(sm)\)
  • \(r(m+n)=rm+rn\)
  • \(1\cdot m=m\)