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    rings and fields

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    (See attached file for full problem description with proper symbols).

    For part one....the first is in rational numbers, and second is in integers.

    ? Verify that is a sub field of and that is a sub ring of .

    ? Let R be a commutative ring and I an ideal of R. let and be elements of R. prove that is then

    ? Let M be an ideal of a commutative ring R and let with . Let . Prove that J is an ideal of R.

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    Solution Summary

    This solution is comprised of a detailed explanation to discuss rings and fields.