Finite depth and Jacobson-Bourbaki correspondence

• Autores: Lars Kadison
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 7, 2008, págs. 1822-1839
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2007.11.007
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• Resumen

  • We introduce a notion of depth three tower CBA with depth two ring extension AB being the case B=C. If and BC is a Frobenius extension with ABC depth three, then AC 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 (ABA)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.