Let R be a ring. For a subset X C R, let (X) denote the ideal generated by X, i.e., the smallest ideal of R that contains X. In class we showed that (X) = = XCI I is the intersection of all ideals of R that contain X. If X and Y are two subsets of R, prove that (XUY) = (X) + (Y).

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Q: Let Q[x] be the ring of polynomials over Q. TRUE or FALSE (with explanation): The principal ideal…

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A: Given  is the ring of polynomials in two variables over  and  be the ideal of R generated by x.…

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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: 8. If 1 and 2 are two ideals of the ring R, prove that the set 1₁+= {x+yx Eh, yЄh} is an ideal of R…

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Q: (10) is maxi

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A: Ideal of a ring

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