# 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.

https://brainmass.com/math/ring-theory/127643

#### 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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