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.
ASJC Scopus subject areas
- Algebra and Number Theory