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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2026 • Question 2

Question

Math 6310 • Algebra Spring 2026 • Question 2

Let \(A := \mathbb {R}[x,y]/(x^2+y^2+1)\). Let \(M \subset A\) be a maximal ideal. Determine the field \(A/M\).

Raw LaTeX

Let \(A := \mathbb{R}[x,y]/(x^2+y^2+1)\). Let \(M \subset A\) be a
maximal ideal. Determine the field \(A/M\).

Topic Tags

Ideals and Quotient Rings Prime and Maximal Ideals