The Structure of F-Pure Rings

Details The Structure of F-Pure Rings The Structure of F-Pure Rings

2003-10-15

arxiv.org/abs/math/0310227v1

Mathematics

Commutative Algebra

15 pages

Scientific paper

For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying how the numbers a_q grow with respect to q. This growth is quantified by the splitting dimension and the splitting ratios of R which we study in detail. We also prove the existence of a special prime ideal P(R) of R, called the splitting prime, that has the property that R/P(R) is strongly F-regular. We show that this ideal captures significant information with regard to the F-purity of R.

Affiliated with

Also associated with

No associations

Rating

The Structure of F-Pure Rings 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 The Structure of F-Pure Rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Structure of F-Pure Rings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-527728