Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 3

Question

Math 6310 • Algebra Summer 2020 • Question 3

Let \(R=\mathbb {Z}[x]\) and suppose that \(I=\langle x\rangle \) and that \(J=\langle x,5\rangle \). How many elements are in \(\operatorname {Tor}^R_i(R/I,R/J)\) for \(i=0,1,2\)?

Raw LaTeX

Let \(R=\mathbb{Z}[x]\) and suppose that \(I=\langle x\rangle\) and that
\(J=\langle x,5\rangle\). How many elements are in \(\operatorname{Tor}^R_i(R/I,R/J)\) for
\(i=0,1,2\)?

Topic Tags

Ideals and Quotient Rings Polynomial Rings and Ring Homomorphism Kernels Tor Functors and Projective Resolutions