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Let R be a commutative ring and let M be an R-module. For a subset S M. The annihilator of S is defined to be
Let R be a commutative ring and let M be an R-module. For a subset S M. The annihilator of S is defined to be Ann(S) := {r R | x S, rx = 0}. Prove that Ann(S) is an ideal of R.
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