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Mat. Sb. (N.S.), 1982, Volume 117(159), Number 1, Pages 60–68 (Mi msb2181)  

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
\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
\jour Math. USSR-Sb.
\yr 1983
\vol 45
\issue 1
\pages 63--71

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    This publication is cited in the following articles:
    1. Wadsworth A., “Dubrovin Valuation Rings and Henselization”, Math. Ann., 283:2 (1989), 301–328  crossref  mathscinet  zmath  isi
    2. A. P. Monastyrnyi, V. I. Yanchevskii, “Whitehead groups of spinor groups”, Math. USSR-Izv., 36:1 (1991), 61–100  mathnet  crossref  mathscinet  zmath  adsnasa
    3. Bill Jacob, Adrian Wadsworth, “Division algebras over Henselian fields”, Journal of Algebra, 128:1 (1990), 126  crossref
    4. Tignol J., “Division-Algebras and Widely Ramified Field-Extensions of Prime Degree”, J. Reine Angew. Math., 404 (1990), 1–38  mathscinet  zmath  isi
    5. Lewis D., Tignol J., “Square Class-Groups and Witt Rings of Central Simple Algebras”, J. Algebra, 154:2 (1993), 360–376  crossref  mathscinet  zmath  isi
    6. 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  crossref  mathscinet  zmath  isi
    7. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    8. R Hazrat, “SK1-like Functors for Division Algebras”, Journal of Algebra, 239:2 (2001), 573  crossref
    9. Hazrat R., “On Central Series of the Multiplicative Group of Division Rings”, Algebr. Colloq., 9:1 (2002), 99–106  mathscinet  zmath  isi
    10. Hazrat R., “Wedderburn's Factorization Theorem Application to Reduced K-Theory”, Proc. Amer. Math. Soc., 130:2 (2002), 311–314  crossref  mathscinet  zmath  isi
    11. Hazrat R., “Reduced K-Theory of Azumaya Algebras”, J. Algebra, 305:2 (2006), 687–703  crossref  mathscinet  zmath  isi
    12. J.-F Renard, J.-R Tignol, A.R. Wadsworth, “Graded Hermitian forms and Springer's theorem”, Indagationes Mathematicae, 18:1 (2007), 97  crossref
    13. Gille Ph., Pianzola A., “Galois Cohomology and Forms of Algebras Over Laurent Polynomial Rings”, Math. Ann., 338:2 (2007), 497–543  crossref  mathscinet  zmath  isi
    14. R. Hazrat, “On the First Galois Cohomology Group of the Algebraic Group SL1(D)”, Communications in Algebra, 36:2 (2008), 381  crossref
    15. J.-P. Tignol, A. R. Wadsworth, “Valuations on algebras with involution”, Math Ann, 2010  crossref
    16. 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  mathnet  crossref
    17. Hazrat R., Wadsworth A.R., “Unitary Sk1 of Graded and Valued Division Algebras”, Proc. London Math. Soc., 103:Part 3 (2011), 508–534  crossref  mathscinet  zmath  isi
    18. Hazrat R., Wadsworth A.R., “Sk1 of Graded Division Algebras”, Isr. J. Math., 183:1 (2011), 117–163  crossref  mathscinet  zmath  isi
    19. 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  crossref
    20. A. R. Wadsworth, “Unitary SK1 of semiramified graded and valued division algebras”, manuscripta math, 139:3-4 (2012), 343  crossref
    21. Mehran Motiee, “On torsion subgroups of whitehead groups of division algebras”, manuscripta math, 2012  crossref
    22. 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  mathnet  crossref  mathscinet
    23. Hazrat R., Wadsworth A.R., “Homogeneous Sk1 of Simple Graded Algebras”, N. Y. J. Math., 18 (2012), 315–336  mathscinet  zmath  isi
    24. R. Hazart, M. Mahdavi-Hezavehi, M. Motiee, “Multiplicative Groups of Division Rings”, Mathematical Proceedings of the Royal Irish Academy, 114:1 (2014), 1  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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