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1. Let M be an R-module and if m0 ∈ M \ {0}, let us denote...

1. Let M be an R-module and if m0 ∈ M \ {0}, let us denote λ (m0): = {x ∈ R: xm0 = 0}.
a) Prove that λ (m0) is a left ideal of R.
b) Furthermore, if M is irreducible and there exists m M and r R such that rm = 0, then λ (m0) is a maximum ideal.
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