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Annihilators and Ideals

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Let R be a commutative ring and let A be any subset of R. The annihilator of A, denoted by Ann(A), is the set {r in R:r(a)=0 for all a in A}. Show that Ann(A) is an ideal of R.

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Solution Summary

Annihilators and ideals are investigated and a step-by-step explanation to the problem is given in the solution. The solution is detailed and well presented.

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We show that Ann(A) is (1) closed under subtraction and (2) closed under multiplication by elements of R.

to this end, let x, y, be in Ann(A) and ...

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