منابع مشابه
Finite depth and Jacobson–Bourbaki correspondence
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 ...
متن کاملGalois Corings and a Jacobson-Bourbaki type Correspondence
The Jacobson-Bourbaki Theorem for division rings was formulated in terms of corings by Sweedler in [14]. Finiteness conditions hypotheses are not required in this new approach. In this paper we extend Sweedler’s result to simple artinian rings using a particular class of corings, comatrix corings. A Jacobson-Bourbaki like correspondence for simple artinian rings is then obtained by duality.
متن کاملThe Ignorance of Bourbaki
If one looks at the history of mathematics, one sees periods of bursting creativity, when new ideas are being developed in a competitive and therefore very hasty spirit; and periods when people find that the ideas so recently in vogue are inexact, incoherent, possibly inconsistent; in such periods there is an urge to consolidate past achievements. I said " the history of mathematics " : but mat...
متن کاملBourbaki ’ s Fixpoint Lemma reconsidered
A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chaincomplete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L. This is then used to deal with coproducts and other aspects of frames.
متن کاملAlec Jacobson Teaching Statement
My passion for teaching began early. Throughout high school and college, I tutored English to African immigrants. Later, while student teaching remedial and gifted-and-talented mathematics at a New York City public middle school, I realized the diversity of how students learn. Some students thrive off interactive lectures, while others do not fully digest a lecture until working out examples at...
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ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 1967
ISSN: 2156-2261
DOI: 10.1215/kjm/1250524337