Depth three towers and Jacobson-Bourbaki correspondence

Details Depth three towers and Jacobson-Bourbaki correspondence Depth three towers and Jacobson-Bourbaki correspondence

2007-06-08

arxiv.org/abs/0706.1215v1

Mathematics

Rings and Algebras

20 pp. (10 pp. supersede math.RA/0703328)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Depth three towers and Jacobson-Bourbaki correspondence 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 Depth three towers and Jacobson-Bourbaki correspondence, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Depth three towers and Jacobson-Bourbaki correspondence will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-653340