Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2018 • Question 8

Question

Math 6310 • Algebra Fall 2018 • Question 8

Let \(R\) be the ring \(\mathbb {Q}[x,y]\), and let \(I\) be the ideal \(I=(x,y)\). What is the \(\mathbb {Q}\)-vector space rank of \(\operatorname {Tor}^{R}_{1}(R/I,I)\)?

Raw LaTeX

Let \(R\) be the ring \(\mathbb{Q}[x,y]\), and let \(I\) be the ideal \(I=(x,y)\). What is the
\(\mathbb{Q}\)-vector space rank of \(\operatorname{Tor}^{R}_{1}(R/I,I)\)?

Topic Tags

Ideals and Quotient Rings Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization Polynomial Rings and Prime Ideals Tor Functors and Projective Resolutions