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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2016 • Question 9

Question

Math 6310 • Algebra Spring 2016 • Question 9

Let \(R=\mathbb {Z}[x]\), set \(I=(x^3)\), and let \(U\) be the multiplicatively closed set \(\{n\in \mathbb {Z}\mid n\text { is odd}\}\). Find all the prime ideals in the ring \((U^{-1}R)/U^{-1}I\).

Raw LaTeX

Let \(R=\mathbb{Z}[x]\), set \(I=(x^3)\), and let \(U\) be the multiplicatively closed set
\(\{n\in\mathbb{Z}\mid n\text{ is odd}\}\). Find all the prime ideals in the ring
\((U^{-1}R)/U^{-1}I\).

Topic Tags

Ideals and Quotient Rings Polynomial Rings and Prime Ideals Polynomial Rings and Ring Homomorphism Kernels Prime and Maximal Ideals