Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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UNRAMIFIED SCALAR EXTENSIONS OF GRADED DIVISION ALGEBRAS

  • Received : 2012.11.14
  • Published : 2014.01.31
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Abstract

Let E be a graded central division algebra (GCDA) over a grade field R. Let S be an unramified graded field extension of R. We describe the grading on the underlying GCDA E' of $E{\otimes}_RS$ which is analogous to the valuation on a tame division algebra over Henselian valued field.

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References

  1. M. Boulagouaz, Le gradue d'une algebre a division valuee, Comm. Algebra 23 (1995), no. 11, 4275-4300. https://doi.org/10.1080/00927879508825464
  2. R. Hazrat and A. R. Wadsworth, $SK_1$ of graded division algebras, Israel J. Math. 183 (2011), 117-163. https://doi.org/10.1007/s11856-011-0045-1
  3. R. Hazrat and A. R. Wadsworth, Unitary $SK_1$ of graded and valued division algebras, Proc. Lond. Math. Soc. 103 (2011), no. 3, 508-534. https://doi.org/10.1112/plms/pdr010
  4. Y.-S. Hwang and A. R. Wadsworth, Algebraic extensions of graded and valued fields, Comm. Algebra 27 (1999), no. 2, 821-840. https://doi.org/10.1080/00927879908826464
  5. Y.-S. Hwang and A. R. Wadsworth, Correspondences between valued division algebras and graded division algebras, J. Algebra 220 (1999), no. 1, 73-114. https://doi.org/10.1006/jabr.1999.7903
  6. B. Jacob and A. R. Wadsworth, Division algebras over Henselian fields, J. Algebra 128 (1990), no.1, 126-179. https://doi.org/10.1016/0021-8693(90)90047-R
  7. M.-A. Knus, A. Merkurjev, M. Rost, and J.-P. Tignol, The Book of Involutions, American Mathematical Society Colloquium Publications, 44. American Mathematical Society, Providence, RI, 1998.
  8. J.-P. Tignol and A. R. Wadsworth, Value functions and associated graded rings for semisimple algebras, Trans. Amer. Math. Soc. 362 (2010), no. 2, 687-726.
  9. A. R. Wadsworth and V. I. Yanchevskii, Unitary $SK_1$ for a graded division ring and its quotient division ring, J. Algebra 352 (2012), 62-78. https://doi.org/10.1016/j.jalgebra.2011.10.044