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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2008 • Question 4

Question

Math 6310 • Algebra Spring 2008 • Question 4

Let \(\omega =-\frac {1}{2}+\frac {\sqrt {-3}}{2}\), a cube root of 1. Show that the ring \(\mathbb {Z}[\sqrt {\omega }]\) is a euclidean domain.

Raw LaTeX

Let \(\omega=-\frac{1}{2}+\frac{\sqrt{-3}}{2}\), a cube root of 1. Show that the ring
\(\mathbb{Z}[\sqrt{\omega}]\) is a euclidean domain.

Topic Tags

Ideals and Quotient Rings Ideals in Quadratic Integer Rings and Exterior Powers