If A, B, C are ideals of a ring R such that BCA, prove that An (B + C) = B+ (AnC) = (An B) + (AnC).
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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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- 17. Suppose is a ring with positive characteristic. Prove that if is any ideal of then is a multiple of the characteristic of.Prove that if a is a unit in a ring R with unity, then a is not a zero divisor.24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set is called the annihilator of in the ring .)