Finite depth and Jacobson–Bourbaki correspondence
نویسنده
چکیده
We introduce a notion of depth three tower C ⊆ B ⊆ A with depth two ring extension A|B being the case B = C . If A = End BC 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 End B AC and coring (A⊗B A) 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. c © 2007 Elsevier B.V. All rights reserved. MSC: Primary: 13B05; 16W30; secondary: 46L37; 81R15
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