TY - JOUR
T1 - Totally positive field extensions and the pythagorean index
AU - Mandal, P.
AU - Preeti, R.
AU - Soman, A.
N1 - Publisher Copyright:
© World Scientific Publishing Company.
PY - 2024/2/1
Y1 - 2024/2/1
N2 - For a formally real field F, we study totally positive field extensions K of F. We prove that, if K/F is Galois and totally positive then so is the corresponding extension of their pythagorean closures Kpy/Fpy. We also study the behavior of weak isotropy and weak hyperbolicity of central simple algebras with an orthogonal involution over totally positive field extensions. We use some of these results and show that a conjecture due to Becher holds in some new cases.
AB - For a formally real field F, we study totally positive field extensions K of F. We prove that, if K/F is Galois and totally positive then so is the corresponding extension of their pythagorean closures Kpy/Fpy. We also study the behavior of weak isotropy and weak hyperbolicity of central simple algebras with an orthogonal involution over totally positive field extensions. We use some of these results and show that a conjecture due to Becher holds in some new cases.
UR - https://www.scopus.com/pages/publications/85143857344
UR - https://www.scopus.com/pages/publications/85143857344#tab=citedBy
U2 - 10.1142/S0219498824500348
DO - 10.1142/S0219498824500348
M3 - Article
AN - SCOPUS:85143857344
SN - 0219-4988
VL - 23
JO - Journal of Algebra and Its Applications
JF - Journal of Algebra and Its Applications
IS - 2
M1 - 2450034
ER -