Prove if c ∈ R is a zero divisor in a commutative ring R, then is c also a divisor in R[x] ? Provide details and explanation
Added by William C.
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An element c ∈ R is a zero divisor if there exists a non-zero element a ∈ R such that ac = 0 or ca = 0. Now, let's consider the polynomial ring R[x]. An element c ∈ R is also an element of R[x] since R is a subring of R[x]. To show that c is a divisor in R[x], we Show more…
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