The corestriction of central simple algebras with dubrovin valuation rings

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Abstract

We analyze the corestriction CorL/F(S) of a central simple algebra S over L with respect to a Dubrovin valuation ring A (resp. Bi) of CORL/F(S) (resp. S) extending V on F (resp. Wi on L) where L is a finite separable extension of F and the Wi are the extensions of V to L for l < i < k. Under the suitable conditions, we show that for the value group, ΓA Σki=1ΓBiand for the center of residue ring, Z(A) C Ar(z(Bi) f|, where At-(Z(Bi) f F) is the normal closure of Z(Bi) over F and miis an integer depending on which roots of unity lie in F and L.

Original languageEnglish
Pages (from-to)2913-2938
Number of pages26
JournalCommunications in Algebra
Volume23
Issue number8
DOIs
Publication statusPublished - 1995

ASJC Scopus subject areas

  • Algebra and Number Theory

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