Correspondences between valued division algebras and graded division algebras

Y. S. Hwang, A. R. Wadsworth

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35 Citations (Scopus)


If D is a tame central division algebra over a Henselian valued field F, then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF. After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map [D] → [GD]g yields an index-preserving isomorphism from the tame part of the Brauer group of F to the graded Brauer group of GF. This isomorphism is shown to be functorial with respect to field extensions and corestrictions, and using this it is shown that there is a correspondence between F-subalgebras of D (with center tame over F) and graded GF-subalgebras of GD.

Original languageEnglish
Pages (from-to)73-114
Number of pages42
JournalJournal of Algebra
Issue number1
Publication statusPublished - 1999 Oct 1

Bibliographical note

Funding Information:
*Supported in part by Grant No. BSRI-97-1408 from the Ministry of Education of Korea. †Supported in part by the NSF.

ASJC Scopus subject areas

  • Algebra and Number Theory


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