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Prove that if R is a commutative ring with unit element then R[x] is also a commutative ring with unit element.

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Modern Algebra
Ring Theory (XXXIX)
Polynomial Rings over Commutative Rings
Unit Element

Prove that R[x] is a commutative ring with unit element whenever R is.
Or,
Prove that if R is a commutative ring with unit element then R[x] is also a commutative ring with unit element.

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Solution Summary

This solution is comprised of a detailed explanation of Polynomial Rings over Commutative Rings. It contains step-by-step explanation that R[x] is a commutative ring with unit element whenever R is.

Solution contains detailed step-by-step explanation.

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See Also This Related BrainMass Solution

If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

Modern Algebra
Ring Theory (XLI)
Polynomial Rings over Commutative rings
Integral Domain
Unit Element
Unit of a Commutative Ring

If R is an integral domain with unit element, prove that any unit in R[x] is a unit in R and any unit in R is also a unit in R[x].

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