Question: Let R be a commutative ring with unity u. a) For any (fixed) a R, prove that aR = {ar| r R] is

Let R be a commutative ring with unity u.
a) For any (fixed) a ∈ R, prove that aR = {ar| r ∈ R] is an ideal of R.
b) If the only ideals of R are {z} and R, prove that R is a field.

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