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Let a and b belong to a commutative ring R. Prove that {x
Chapter 14, Problem 44E(choose chapter or problem)
QUESTION:
Problem 44E
Let a and b belong to a commutative ring R. Prove that {x ∈ R | ax ∈ bR} is an ideal.
Questions & Answers
QUESTION:
Problem 44E
Let a and b belong to a commutative ring R. Prove that {x ∈ R | ax ∈ bR} is an ideal.
ANSWER:Step 1 of 2
We use Ideal Test to prove that is an ideal of .
First take any two ; then we have , which means there are some such that and .
Now we compute the difference
because . This proves that .