On the homology of regular quotients
Andrew Baker
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland.
a.baker@maths.gla.ac.uk
We construct a free resolution of $R/I^s$ over $R$ where $I\ideal R$ is
generated by a (finite or infinite) regular sequence. This generalizes
the Koszul complex for the case $s=1$. We easily deduce that for $s>1$,
the algebra structure of $\Tor^R_*(R/I,R/I^s)$ is trivial and the reduction
$R/I^s\lra R/I^{s-1}$ induces the trivial map of algebras.