5.Let R be a commutative ring and a any element in R. Define the annhilator of a to be the set ann(a) = {r ∈ R | ra = 0}(that is, the set of all elements that multiply ato zero). Prove that ann(a)is an ideal of R.

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Q: Let R be a ring. If the only ideals of R are {0} and R itself, then R is a field.

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Q: If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+(AnC) = (A B) + (AnC).

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Q: 5. Let R be a ring and I, J ideals of R. Is IUJ always an ideal of R? Either prove that this is the…

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Q: 1. Let / be a subset of the ring R. Prove that I is an ideal of R if and only if I is nonempty and x…

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