Depth three towers and Jacobson-Bourbaki correspondence
| dc.creator | Kadison, Lars | |
| dc.date | 2007-06-08 | |
| dc.date.accessioned | 2026-07-07T08:04:41Z | |
| dc.date.available | 2026-07-07T08:04:41Z | |
| dc.description | We introduce a notion of depth three tower of three rings C < B < A as a useful generalization of depth two ring extension. If A = End B_C and B | C is a Frobenius extension, this also captures the notion of depth three for a Frobenius extension in math.RA/0107064 and math.RA/0108067 such that if B | C is depth three, then A | C is depth two (cf. math.QA/0001020). If A, B and C correspond to a tower of subgroups G > H > K via the group algebra over a fixed base ring, the depth three condition is the condition that subgroup K has normal closure K^G contained in H. For a depth three tower of rings, there is a pre-Galois theory for the ring End {}_BA_C and coring (A \otimes_B A)^C involving Morita context bimodules and left coideal subrings. This is applied in the last two sections to a specialization of a Jacobson-Bourbaki correspondence theorem for augmented rings to depth two extensions with depth three intermediate division rings. | |
| dc.description | 20 pp. (10 pp. supersede math.RA/0703328) | |
| dc.identifier | https://arxiv.org/abs/0706.1215 | |
| dc.identifier | http://arxiv.org/abs/0706.1215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130052 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Commutative Algebra | |
| dc.subject | (Primary) 13B05, 16W30, 81R15; (Secondary) 46L37 | |
| dc.title | Depth three towers and Jacobson-Bourbaki correspondence | |
| dc.type | text |