The corestriction of central simple algebras with dubrovin valuation rings

Yoon Sung Hwang

doi:10.1080/00927879508825377

The corestriction of central simple algebras with dubrovin valuation rings

Yoon Sung Hwang

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	2913-2938
Number of pages	26
Journal	Communications in Algebra
Volume	23
Issue number	8
DOIs	https://doi.org/10.1080/00927879508825377
Publication status	Published - 1995 Jan

Bibliographical note

Funding Information:
*This author was partially supported b y the Global Ar~alpsisResearch Ccnter 111 Seoul, Korea.

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927879508825377

Cite this

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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.",

author = "Hwang, {Yoon Sung}",

note = "Funding Information: *This author was partially supported b y the Global Ar~alpsisResearch Ccnter 111 Seoul, Korea.",

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Y1 - 1995/1

N2 - 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.

AB - 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.

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The corestriction of central simple algebras with dubrovin valuation rings

Abstract

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