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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2010 • Question 7

Question

Math 6310 • Algebra Fall 2010 • Question 7

Let \(\alpha \) be the positive real root of \(x^6-7\). What is the number of elements of the ring \(\mathbb {Z}[\alpha ]/(\alpha ^2)\)? Is every ideal in this ring principal?

Raw LaTeX

Let \(\alpha\) be the positive real root of \(x^6-7\). What is the number of elements of the ring
\(\mathbb{Z}[\alpha]/(\alpha^2)\)? Is every ideal in this ring principal?

Topic Tags

Ideals and Quotient Rings Polynomial Rings and Prime Ideals