TY - JOUR
T1 - Division algebras with common subfields
AU - Krashen, Daniel
AU - Matzri, Eliyahu
AU - Rapinchuk, Andrei
AU - Rowen, Louis
AU - Saltman, David
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/9/1
Y1 - 2022/9/1
N2 - 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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85110882276
U2 - 10.1007/s00229-021-01315-5
DO - 10.1007/s00229-021-01315-5
M3 - Article
AN - SCOPUS:85110882276
SN - 0025-2611
VL - 169
SP - 209
EP - 249
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
IS - 1-2
ER -