The Structure of F-Pure Rings
| dc.creator | Aberbach, Ian M. | |
| dc.creator | Enescu, Florian | |
| dc.date | 2003-10-15 | |
| dc.date.accessioned | 2026-07-07T05:01:56Z | |
| dc.date.available | 2026-07-07T05:01:56Z | |
| dc.description | 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. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310227 | |
| dc.identifier | http://arxiv.org/abs/math/0310227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68863 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A35 | |
| dc.title | The Structure of F-Pure Rings | |
| dc.type | text |