Abstract:
In this paper the group $SK_1(A)$ is computed for a division ring $A$ whose center has a nontrivial Henselian valuation.
Bibliography: 17 titles.
\Bibitem{Ers82}
\by Yu.~L.~Ershov
\paper Henselian valuations of division rings and the group $SK_1$
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 1
\pages 63--71
\mathnet{http://mi.mathnet.ru/eng/sm2181}
\crossref{https://doi.org/10.1070/SM1983v045n01ABEH000992}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=642489}
\zmath{https://zbmath.org/?q=an:0514.16013|0508.16017}
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This publication is cited in the following 30 articles:
Mehran Motiee, “On the exponent of a certain quotient of Whitehead groups of division algebras”, Communications in Algebra, 2024, 1
V. I. Yanchevskiǐ, “Henselian division algebras and reduced unitary Whitehead groups for outer forms of anisotropic algebraic groups of the type $A_n$”, Sb. Math., 213:8 (2022), 1096–1156
I. O. Govorushko, V. I. Yanchevskii, “On the classification of finite-dimensional Henselian simple central algebras with unitary involutions”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 56:2 (2020), 135
Abhay Soman, “On triviality of the reduced Whitehead group over Henselian fields”, Arch. Math., 113:3 (2019), 237
V. I. Yanchevskiǐ, “Tate cohomology of special norm modules related to Henselian division algebras”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 54:3 (2018), 273
R. Hazart, M. Mahdavi-Hezavehi, M. Motiee, “Multiplicative Groups of Division Rings”, Mathematical Proceedings of the Royal Irish Academy, 114:1 (2014), 1
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A. R. Wadsworth, “Unitary SK1 of semiramified graded and valued division algebras”, manuscripta math, 139:3-4 (2012), 343
Mehran Motiee, “On torsion subgroups of whitehead groups of division algebras”, manuscripta math, 2012
V. I. Yanchevskii, “Reduced Whitehead groups and conjugacy problem for special unitary groups of anisotropic hermitian forms”, J. Math. Sci. (N. Y.), 192:2 (2013), 250–262
Hazrat R., Wadsworth A.R., “Homogeneous Sk1 of Simple Graded Algebras”, N. Y. J. Math., 18 (2012), 315–336
V. I. Yanchevskiǐ, “Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups”, J. Math. Sci. (N. Y.), 183:5 (2012), 727–747
Hazrat R., Wadsworth A.R., “Unitary Sk1 of Graded and Valued Division Algebras”, Proc. London Math. Soc., 103:Part 3 (2011), 508–534
Hazrat R., Wadsworth A.R., “Sk1 of Graded Division Algebras”, Isr. J. Math., 183:1 (2011), 117–163
J.-P. Tignol, A. R. Wadsworth, “Valuations on algebras with involution”, Math Ann, 2010
R. Hazrat, “On the First Galois Cohomology Group of the Algebraic Group SL1(D)”, Communications in Algebra, 36:2 (2008), 381
J.-F Renard, J.-R Tignol, A.R. Wadsworth, “Graded Hermitian forms and Springer's theorem”, Indagationes Mathematicae, 18:1 (2007), 97
Gille Ph., Pianzola A., “Galois Cohomology and Forms of Algebras Over Laurent Polynomial Rings”, Math. Ann., 338:2 (2007), 497–543
Hazrat R., “Reduced K-Theory of Azumaya Algebras”, J. Algebra, 305:2 (2006), 687–703
Hazrat R., “On Central Series of the Multiplicative Group of Division Rings”, Algebr. Colloq., 9:1 (2002), 99–106
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