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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2021 • Question 1

Question

Math 6310 • Algebra Fall 2021 • Question 1

Consider the ring homomorphism given by

\[ \begin {aligned} \mathbb {Z}[x]&\longrightarrow \mathbb {Q}\\ f(x)&\longmapsto f(1/2). \end {aligned} \]

Determine a minimal generating set for the kernel.

Raw LaTeX

Consider the ring homomorphism given by

\[
\begin{aligned}
\mathbb{Z}[x]&\longrightarrow \mathbb{Q}\\
f(x)&\longmapsto f(1/2).
\end{aligned}
\]


Determine a minimal generating set for the kernel.

Topic Tags

Hom Functors and Module Homomorphisms Polynomial Rings and Ring Homomorphism Kernels