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This article is cited in 23 scientific papers (total in 24 papers)
Henselian valuations of division rings and the group $SK_1$
Yu. L. Ershov
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.
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English version:
Mathematics of the USSR-Sbornik, 1983, 45:1, 63–71
Bibliographic databases:
 
UDC:
513.6
MSC: Primary 12E15, 12J10, 18F25; Secondary 13J15
Received: 02.04.1980
Citation:
Yu. L. Ershov, “Henselian valuations of division rings and the group $SK_1$”, Mat. Sb. (N.S.), 117(159):1 (1982), 60–68; Math. USSR-Sb., 45:1 (1983), 63–71
Citation in format AMSBIB
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\by Yu.~L.~Ershov
\paper Henselian valuations of division rings and the group $SK_1$
\jour Mat. Sb. (N.S.)
\yr 1982
\vol 117(159)
\issue 1
\pages 60--68
\mathnet{http://mi.mathnet.ru/msb2181}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=642489}
\zmath{https://zbmath.org/?q=an:0514.16013|0508.16017}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 1
\pages 63--71
\crossref{https://doi.org/10.1070/SM1983v045n01ABEH000992}
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Wadsworth A., “Dubrovin Valuation Rings and Henselization”, Math. Ann., 283:2 (1989), 301–328
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Chacron M., Dherte H., Tignol J., Wadsworth A., Yanchevskii V., “Discriminants of Involutions on Henselian Division-Algebras”, Pac. J. Math., 167:1 (1995), 49–79
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S. S. Goncharov, I. A. Lavrov, V. D. Mazurov, A. A. Mal'tsev, A. S. Morozov, A. A. Nikitin, E. A. Palyutin, D. M. Smirnov, “Yuri Leonidovich Ershov (on his 60th birthday)”, Russian Math. Surveys, 55:6 (2000), 1193–1204
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R Hazrat, “SK1-like Functors for Division Algebras”, Journal of Algebra, 239:2 (2001), 573
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Hazrat R., “On Central Series of the Multiplicative Group of Division Rings”, Algebr. Colloq., 9:1 (2002), 99–106
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Hazrat R., “Wedderburn's Factorization Theorem Application to Reduced K-Theory”, Proc. Amer. Math. Soc., 130:2 (2002), 311–314
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J.-F Renard, J.-R Tignol, A.R. Wadsworth, “Graded Hermitian forms and Springer's theorem”, Indagationes Mathematicae, 18:1 (2007), 97
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Gille Ph., Pianzola A., “Galois Cohomology and Forms of Algebras Over Laurent Polynomial Rings”, Math. Ann., 338:2 (2007), 497–543
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R. Hazrat, “On the First Galois Cohomology Group of the Algebraic Group SL1(D)”, Communications in Algebra, 36:2 (2008), 381
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J.-P. Tignol, A. R. Wadsworth, “Valuations on algebras with involution”, Math Ann, 2010
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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
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Hazrat R., Wadsworth A.R., “Unitary Sk1 of Graded and Valued Division Algebras”, Proc. London Math. Soc., 103:Part 3 (2011), 508–534
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Hazrat R., Wadsworth A.R., “Sk1 of Graded Division Algebras”, Isr. J. Math., 183:1 (2011), 117–163
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M. Mahdavi-Hezavehi, M. Motiee, “A Criterion for the Triviality ofG(D) and Its Applications to the Multiplicative Structure ofD”, Communications in Algebra, 40:7 (2012), 2645
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A. R. Wadsworth, “Unitary SK1 of semiramified graded and valued division algebras”, manuscripta math, 139:3-4 (2012), 343
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Mehran Motiee, “On torsion subgroups of whitehead groups of division algebras”, manuscripta math, 2012
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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
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Hazrat R., Wadsworth A.R., “Homogeneous Sk1 of Simple Graded Algebras”, N. Y. J. Math., 18 (2012), 315–336
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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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