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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2021 • Question 4

Question

Math 6310 • Algebra Fall 2021 • Question 4

Let \(I\) be the ideal \((2,1+\sqrt {-5})\) in the ring \(R:=\mathbb {Z}[\sqrt {-5}]\), 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 \((2,1+\sqrt{-5})\) in the ring \(R:=\mathbb{Z}[\sqrt{-5}]\), 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