Mathematics – Commutative Algebra
Scientific paper
2002-07-12
Mathematics
Commutative Algebra
revised version, incorporating referee's comments, LaTeX, 10 pages
Scientific paper
Let $R=k[x_1, ..., x_n]/(x_1^d + ... + x_n^d)$, where $k$ is a field of characteristic $p$, $p$ does not divide $d$ and $n \geq 3$. We describe a method for computing the test ideal for these diagonal hypersurface rings. This method involves using a characterization of test ideals in Gorenstein rings as well as developing a way to compute tight closures of certain ideals despite the lack of a general algorithm. In addition, we compute examples of test ideals in diagonal hypersurface rings of small characteristic (relative to $d$) including several that are not integrally closed. These examples provide a negative answer to Smith's (2000, Comm. in Alg.) question of whether the test id eal in general is always integrally closed.
No associations
LandOfFree
Test ideals in diagonal hypersurface rings II 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 Test ideals in diagonal hypersurface rings II, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Test ideals in diagonal hypersurface rings II will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-710251