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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2007 • Question 9

Question

Math 6310 • Algebra Fall 2007 • Question 9

Let \(m\) be a maximal ideal in \(\mathbb {R}[x,y]\) containing \(x^2+y^2+1\). What is the quotient \(\mathbb {R}[x,y]/m\)? Justify your answer.

Raw LaTeX

Let \(m\) be a maximal ideal in \(\mathbb{R}[x,y]\) containing \(x^2+y^2+1\). What is the quotient
\(\mathbb{R}[x,y]/m\)? Justify your answer.

Topic Tags

Ideals and Quotient Rings Prime and Maximal Ideals