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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2009 • Question 6

Question

Math 6310 • Algebra Spring 2009 • Question 6

Let \(\mathfrak {a}\) be the ideal of the polynomial ring \(\mathbb {R}[x]\) that is generated by \(x^3-5x^2+6x-2\) and \(x^4-4x^3+3x^2-4x+2\). Is \(\mathfrak {a}\) a principal ideal? Is it prime? Is it maximal?

Raw LaTeX

Let \(\mathfrak{a}\) be the ideal of the polynomial ring \(\mathbb{R}[x]\) that is generated by
\(x^3-5x^2+6x-2\) and \(x^4-4x^3+3x^2-4x+2\). Is \(\mathfrak{a}\) a principal ideal? Is it prime?
Is it maximal?

Topic Tags

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