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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2023 • Question 3

Question

Math 6310 • Algebra Fall 2023 • Question 3

Suppose \(R=\mathbb {Q}[x,y]\) is a polynomial ring. Compute the \(\mathbb {Q}\)-vector space dimension of \[ \operatorname {Tor}^R_1\left (\operatorname {Ext}^1_R(R/(x^2),R/(y^2)),R/(y)\right ). \]

Raw LaTeX

Suppose \(R=\mathbb{Q}[x,y]\) is a polynomial ring. Compute the \(\mathbb{Q}\)-vector space dimension of
\[
\operatorname{Tor}^R_1\left(\operatorname{Ext}^1_R(R/(x^2),R/(y^2)),R/(y)\right).
\]

Topic Tags

Ext Functors and Module Extensions Polynomial Rings and Ring Homomorphism Kernels Tor Functors and Projective Resolutions