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Galois theory and Lubin-Tate cochains on classifying spaces

Andrew Baker, Birgit Richter (2011)

Open Mathematics

We consider brave new cochain extensions F(BG +,R) → F(EG +,R), where R is either a Lubin-Tate spectrum E n or the related 2-periodic Morava K-theory K n, and G is a finite group. When R is an Eilenberg-Mac Lane spectrum, in some good cases such an extension is a G-Galois extension in the sense of John Rognes, but not always faithful. We prove that for E n and K n these extensions are always faithful in the K n local category. However, for a cyclic p-group C p r , the cochain extension F ( B C p r + , E n ) F ( E C p r + , E n ) is not a Galois...

Generalization of the S -Noetherian concept

Abdelamir Dabbabi, Ali Benhissi (2023)

Archivum Mathematicum

Let A be a commutative ring and 𝒮 a multiplicative system of ideals. We say that A is 𝒮 -Noetherian, if for each ideal Q of A , there exist I 𝒮 and a finitely generated ideal F Q such that I Q F . In this paper, we study the transfer of this property to the polynomial ring and Nagata’s idealization.

Graded morphisms of G -modules

Hanspeter Kraft, Claudio Procesi (1987)

Annales de l'institut Fourier

Let A be finite dimensional C -algebra which is a complete intersection, i.e. A = C [ X 1 , ... , X n ] / ( f 1 , ... , f n ) whith a regular sequences f 1 , ... , f n . Steve Halperin conjectured that the connected component of the automorphism group of such an algebra A is solvable. We prove this in case A is in addition graded and generated by elements of degree 1.

Homotopy representability of Brauer groups.

Antonio Martínez Cegarra (1999)

Extracta Mathematicae

The purpose of this paper is to present certain facts and results showing a way through which simplicial homotopy theory can be used in the study of Auslander-Goldman-Brauer groups of Azumaya algebras over commutative rings.

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