Question: (a) Let (R, +, ) be a finite commutative ring with unity u. If r R and r is not the zero element of

(a) Let (R, +, •) be a finite commutative ring with unity u. If r ∈ R and r is not the zero element of R, prove that r is either a unit or a proper divisor of zero.
(b) Does the result in part (a) remain valid when R is infinite?

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