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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2014 • Question 7

Question

Math 6310 • Algebra Fall 2014 • Question 7

Determine, in each case, whether the given ring is a unique factorization domain:

  1. \(\mathbb {Z}[\sqrt {-1}]\),
  2. \(\mathbb {Z}[\sqrt {-5}]\),
  3. \(\mathbb {Z}[2\sqrt {2}]\)

Raw LaTeX

Determine, in each case, whether the given ring is a unique factorization domain:
\begin{enumerate}
\item
\(\mathbb{Z}[\sqrt{-1}]\),

\item
\(\mathbb{Z}[\sqrt{-5}]\),

\item
\(\mathbb{Z}[2\sqrt{2}]\)
\end{enumerate}

Topic Tags

Ideals in Quadratic Integer Rings and Exterior Powers