Let A be a commutative ring with identity 1, and let A[x] be the ring of polynomials with coefficients in A.
Let f (x) = a0+ a1x + ... + anxn! A[x] .
Prove that f (x) is a zero - divisor in A[x] IF AND ONLY IF (iff) 7c ! A, c ! 0 " cf (x) = 0.
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Commutative rings and a zero-divisor are investigated. The solution is detailed and well presented.