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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 4

Question

Math 6310 • Algebra Summer 2020 • Question 4

Let \(I\) be the ideal \((x,y)\) in the polynomial ring \(R:=\mathbb {C}[x,y]\), and let \(\Lambda ^2(I)\) denote the second exterior power of \(I\) in the category of \(R\)-modules. Prove or disprove: \(\Lambda ^2(I)\) is zero.

Raw LaTeX

Let \(I\) be the ideal \((x,y)\) in the polynomial ring \(R:=\mathbb{C}[x,y]\), and let
\(\Lambda^2(I)\) denote the second exterior power of \(I\) in the category of \(R\)-modules.
Prove or disprove: \(\Lambda^2(I)\) is zero.

Topic Tags

Ideals and Quotient Rings Ideals in Quadratic Integer Rings and Exterior Powers Polynomial Rings and Prime Ideals Polynomial Rings and Ring Homomorphism Kernels