Mathematics – Commutative Algebra
Scientific paper
2004-09-04
Mathematics
Commutative Algebra
2 pages
Scientific paper
Let $(A,\mathfrak{m})$ be a Noetherian local ring, $M$ a finite $A$-module
and $x_1,...,x_n\in \m$ such that $\lambda (M/\x M)$ is finite. Serre proved
that all partial Euler characteristics of $M$ with respect to $\x$ is
non-negative. This fact is easy to show when $A$ contains a field. We give an
elementary proof of Serre's result when $A$ does not contain a field.
No associations
LandOfFree
A short note on the non-negativity of partial Euler characteristics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A short note on the non-negativity of partial Euler characteristics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A short note on the non-negativity of partial Euler characteristics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-325798