UNRAMIFIED SCALAR EXTENSIONS OF GRADED DIVISION ALGEBRAS Hwang, Yoon Sung;
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 which is analogous to the valuation on a tame division algebra over Henselian valued field.
graded central division algebras;graded fields;unramified extension;
M. Boulagouaz, Le gradue d'une algebre a division valuee, Comm. Algebra 23 (1995), no. 11, 4275-4300.
R. Hazrat and A. R. Wadsworth, $SK_1$ of graded division algebras, Israel J. Math. 183 (2011), 117-163.
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.
Y.-S. Hwang and A. R. Wadsworth, Algebraic extensions of graded and valued fields, Comm. Algebra 27 (1999), no. 2, 821-840.
Y.-S. Hwang and A. R. Wadsworth, Correspondences between valued division algebras and graded division algebras, J. Algebra 220 (1999), no. 1, 73-114.
B. Jacob and A. R. Wadsworth, Division algebras over Henselian fields, J. Algebra 128 (1990), no.1, 126-179.
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.
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.
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.