Mathematics Homework Solutions
Problem
#53428

rings and fields

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

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


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• 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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. Prove that J is an ideal of R.

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This solution is comprised of a detailed explanation to
• 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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