منابع مشابه
The Endomorphism Ring Theorem for Galois and D2 Extensions
Let S be the left bialgebroid End BAB over the centralizer R of a right D2 algebra extension A | B, which is to say that its tensor-square is isomorphic as A-B-bimodules to a direct summand of a finite direct sum of A with itself. Without an antipode, we prove that the left endomorphism algebra is a left S-Galois extension of A, and find a formula for the inverse Galois mapping. As a corollary,...
متن کاملRealizability of Algebraic Galois Extensions by Strictly Commutative Ring Spectra
We discuss some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups and to global Galois extensions. We describe parts of the general framework developed by Rognes. Central rôles are played by the notion of strong duality and a trace mapping constructed by Greenlees and May in the context ...
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Introduction. Galois extensions of noncommutative rings were introduced in 1964 by Teruo Kanzaki [13]. These algebraic objects generalize to noncommutative rings the classical Galois extensions of fields and the Galois extensions of commutative rings due to Auslander and Goldman [1]. At the same time they also turn out to be fundamental examples of Hopf-Galois extensions; these were first consi...
متن کاملRealisibility of Algebraic Galois Extensions by Strictly Commutative Ring Spectra
We describe some of the basic ideas of Galois theory for commutative S-algebras originally formulated by John Rognes. We restrict attention to the case of finite Galois groups. We describe the general framework developed by Rognes. Central rôles are played by the notion of strong duality and a trace or norm mapping constructed by Greenlees and May in the context of generalized Tate cohomology. ...
متن کاملExtensions of Galois Connections
Galois connections play a very important role in the theory of continuous lattices and their various generalizations. (See, for example, [1], [2], [a], [4], [5], [7] and [9].) Morphisms of continuous lattices, as defined in [2], are precisely those upper adjoints of Galois connections which preserve directed sups. In [1] Bandelf and Ernd suggested that the right choice of morphisms for Z-contin...
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ژورنال
عنوان ژورنال: Acta Physica Polonica A
سال: 2017
ISSN: 0587-4246,1898-794X
DOI: 10.12693/aphyspola.132.97