대한수학회지 (Journal of the Korean Mathematical Society)

  • 제34권2호
  • /
  • Pages.279-284
  • /
  • 1997
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

THE INDEX OF THE CORESTRICTION OF A VALUED DIVISION ALGEBRA

  • 발행 : 1997.05.01
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초록

Let L/F be a finite separable extension of Henselian valued fields with same residue fields $\overline{L} = \overline{F}$. Let D be an inertially split division algebra over L, and let $^cD$ be the underlying division algebra of the corestriction $cor_{L/F} (D)$ of D. We show that the index $ind(^cD) of ^cD$ divides $[Z(\overline{D}) : Z(\overline {^cD})] \cdot ind(D), where Z(\overline{D})$ is the center of the residue division ring $\overline{D}$.

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참고문헌

  1. London Math. Soc. Lecture Note Series, 81 Skew Fields P. Draxl
  2. Pacific J. Math. v.170 The corestriction of valued division algebras over Henselin Fields II Y. Hwang
  3. J.Algebra v.128 Division algebras over Henselian fields B. Jacob;A.Wadsworth
  4. Associative Algebras R. S. Pierce
  5. Maximal Orders I. Reiner
  6. Expositiones Math. v.3 Equivalent forms of Hensel’s lemma P. Ribenboim
  7. Math. v.11 The corestriction of algebraic structures, Inventiones C. Riehm
  8. Proc. Amer. Math. Soc. v.98 Extending valuations to finite dimensional division algebras A. Wadsworth