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Algebra Logika, 2004, Volume 43, Number 3, Pages 353–363 (Mi al77)  

This article is cited in 6 scientific papers (total in 7 papers)

Constructive Matrix and Orderable Groups

V. A. Roman'kov, N. G. Khisamiev


Abstract: We study into the relationship between constructivizations of an associative commutative ring $K$ with unity and constructivizations of matrix groups $GL_n(K)$ (general), $SL_n(K)$ (special), and $UT_n(K)$ (unitriangular) over $K$. It is proved that for $n\geqslant3$, a corresponding group is constructible iff so is $K$. We also look at constructivizations of ordered groups. It turns out that a torsion-free constructible Abelian group is orderly constructible. It is stated that the unitriangular matrix group $UT_n(K)$ over an orderly constructible commutative associative ring $K$ is itself orderly constructible. A similar statement holds also for finitely generated nilpotent groups, and countable free nilpotent groups.

Keywords: matrix group, ordered group, constructivization, orderly constructive system

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English version:
Algebra and Logic, 2004, 43:3, 198–204

Bibliographic databases:

UDC: 512.540+510.5
Received: 05.06.2002

Citation: V. A. Roman'kov, N. G. Khisamiev, “Constructive Matrix and Orderable Groups”, Algebra Logika, 43:3 (2004), 353–363; Algebra and Logic, 43:3 (2004), 198–204

Citation in format AMSBIB
\Bibitem{RomKhi04}
\by V.~A.~Roman'kov, N.~G.~Khisamiev
\paper Constructive Matrix and Orderable Groups
\jour Algebra Logika
\yr 2004
\vol 43
\issue 3
\pages 353--363
\mathnet{http://mi.mathnet.ru/al77}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2084041}
\zmath{https://zbmath.org/?q=an:1080.20044}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 3
\pages 198--204
\crossref{https://doi.org/10.1023/B:ALLO.0000028933.64042.93}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249087650}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. G. Khisamiev, “On constructive nilpotent groups”, Siberian Math. J., 48:1 (2007), 172–179  mathnet  crossref  mathscinet  zmath  isi
    2. N. G. Khisamiev, “Torsion-free constructive nilpotent $R_p$-groups”, Siberian Math. J., 50:1 (2009), 181–187  mathnet  crossref  mathscinet  isi
    3. N. G. Khisamiev, “On positive and constructive groups”, Siberian Math. J., 53:5 (2012), 906–917  mathnet  crossref  mathscinet  isi  elib
    4. M. K. Nurizinov, R. K. Tyulyubergenev, N. G. Khisamiev, “Computable torsion-free nilpotent groups of finite dimension”, Siberian Math. J., 55:3 (2014), 471–481  mathnet  crossref  mathscinet  isi  elib
    5. Tyulyubergenev R.K., “On Computable Subgroups of the Group of All Unitriangular Matrices Over a Ring”, Bull. Karaganda Univ-Math., 86:2 (2017), 74–78  isi
    6. Khisamiev N.G. Latkin I.V., “On Constructive Nilpotent Groups”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, ed. Day A. Fellows M. Greenberg N. Khoussainov B. Melnikov A. Rosamond F., Springer International Publishing Ag, 2017, 324–353  crossref  mathscinet  zmath  isi  scopus
    7. B. S. Baizhanov, B. Sh. Kulpeshov, T. S. Zambarnaya, “A.D. Taimanov and model theory in Kazakhstan”, Sib. elektron. matem. izv., 17 (2020), 1–58  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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