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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1996 • Question 6

Question

Math 6310 • Algebra Fall 1996 • Question 6

Let \(P_\bullet \) be a complex of projective modules with \(P_n=0\) for \(n<0\). Let \(E_\bullet \) be an exact complex. Show that any map of complexes from \(P_\bullet \) to \(E_\bullet \) is homotopic to zero.

Raw LaTeX

Let \(P_\bullet\) be a complex of projective modules with \(P_n=0\) for \(n<0\). Let \(E_\bullet\) be an
exact complex. Show that any map of complexes from \(P_\bullet\) to \(E_\bullet\) is homotopic to
zero.

Topic Tags

Exact Sequences of Modules Projective Modules Tor Functors and Projective Resolutions