Chapter 8.1, Problem 23E

Describe the kernel of epimorphism $\varphi$ in Exercise 22.

Assume that each of $R$ and $S$ is a commutative ring with unity and that $\theta :R\to S$ is an epimorphism from $R$ to $S$. Let $\varphi :R\left[x\right]\to S\left[x\right]$ be defined by, $\varphi \left(a_0+a_{1}x+\cdot \cdot \cdot +a_n{x}^n\right)=\theta \left(a_0\right)+\theta \left(a_1\right)x+\cdot \cdot \cdot +\theta \left(a_n\right)x^n$.