Division algebras with common subfields

Daniel Krashen, Eliyahu Matzri, Andrei Rapinchuk, Louis Rowen, David Saltman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study the partial ordering on isomorphism classes of central simple algebras over a given field F, defined by setting A1≤ A2 if deg A1= deg A2 and every étale subalgebra of A1 is isomorphic to a subalgebra of A2, and generalizations of this notion to algebras with involution. In particular, we show that this partial ordering is invariant under passing to the completion of the base field with respect to a discrete valuation, and we explore how this partial ordering relates to the exponents of algebras.

Original languageEnglish
Pages (from-to)209-249
Number of pages41
JournalManuscripta Mathematica
Volume169
Issue number1-2
DOIs
StatePublished - Sep 2022

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

This work was supported by the U.S.-Israel Binational Science Foundation (Grant No. 201049) and by the Israel Science Foundation (Grant No. 630/17)

FundersFunder number
United States - Israel Binational Science Foundation
United States-Israel Binational Science Foundation201049
Israel Science Foundation630/17

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