### 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 | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**The corestriction of central simple algebras with dubrovin valuation rings.** / Hwang, Yoon Sung.

Research output: Contribution to journal › Article

*Communications in Algebra*, vol. 23, no. 8, pp. 2913-2938. https://doi.org/10.1080/00927879508825377

}

TY - JOUR

T1 - The corestriction of central simple algebras with dubrovin valuation rings

AU - Hwang, Yoon Sung

PY - 1995

Y1 - 1995

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.

UR - http://www.scopus.com/inward/record.url?scp=84972922096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972922096&partnerID=8YFLogxK

U2 - 10.1080/00927879508825377

DO - 10.1080/00927879508825377

M3 - Article

AN - SCOPUS:84972922096

VL - 23

SP - 2913

EP - 2938

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 8

ER -