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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2022 • Question 3

Question

Math 6310 • Algebra Fall 2022 • Question 3

Let \(R=\mathbb {R}[x,y]\), let \(I=(x,y)\) be the ideal generated by \(x\) and \(y\) and let \(M=R/I\). Compute \(\dim _{\mathbb {R}}\operatorname {Tor}^R_i(I,M)\) for all \(i\).

Raw LaTeX

Let \(R=\mathbb{R}[x,y]\), let \(I=(x,y)\) be the ideal generated by \(x\) and \(y\) and let \(M=R/I\). Compute \(\dim_{\mathbb{R}}\operatorname{Tor}^R_i(I,M)\) for
all \(i\).

Topic Tags

Ideals and Quotient Rings Tor Functors and Projective Resolutions