A student is asked to prove that a quotient ring of a ring R modulo an ideal
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A student is asked to prove that a quotient ring of a ring R modulo an ideal N is commutative if and only if (rs - sr) ∈ N for all r, s ∈ R. The student starts out: Assume R/ N is commutative. Then rs = sr for all r, s ∈ R/N.
a. Why does the instructor reading this expect nonsense from there on?
b. What should the student have written?
c. Prove the assertion. (Note the "if and only if.")
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a The notations r and s would be used to denote elements of R not of RN The student prob...View the full answer
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