Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(4): 939-959

Online first article July 9, 2019      Printed July 31, 2019

https://doi.org/10.4134/BKMS.b180722

Copyright © The Korean Mathematical Society.

On generalized graded crossed products and Kummer subfields of simple algebras

Driss Bennis, Karim Mounirh, Fouad Taraza

Research Center CeReMAR; Research Center CeReMAR; Research Center CeReMAR

Abstract

{\normalsize } Using generalized graded crossed products, we give necessary and sufficient conditions for a simple algebra over a Henselian valued field (under some hypotheses) to have Kummer subfields. This study generalizes some known works. We also study many properties of generalized graded crossed products and conditions for embedding a graded simple algebra into a matrix algebra of a graded division ring.

Keywords: generalized graded crossed products, simple algebra, Henselian valued field, graded division ring

MSC numbers: 16K50, 16W50, 16W60, 16W70

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