Finite depth and Jacobson-Bourbaki correspondence |
| |
Authors: | Lars Kadison |
| |
Institution: | Department of Mathematics, University of Pennsylvania, David Rittenhouse Lab, 209 S. 33rd St., Philadelphia, PA 19104, United States |
| |
Abstract: | We introduce a notion of depth three tower C⊆B⊆A with depth two ring extension A|B being the case B=C. If and B|C is a Frobenius extension with A|B|C depth three, then A|C is depth two. If A, B and C correspond to a tower G>H>K via group algebras over a base ring F, the depth three condition is the condition that K has normal closure KG contained in H. For a depth three tower of rings, a pre-Galois theory for the ring and coring (A⊗BA)C involving Morita context bimodules and left coideal subrings is applied to specialize a Jacobson-Bourbaki correspondence theorem for augmented rings to depth two extensions with depth three intermediate division rings. |
| |
Keywords: | Primary 13B05 16W30 secondary 46L37 81R15 |
本文献已被 ScienceDirect 等数据库收录! |
|