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Fundam. Prikl. Mat., 2004, Volume 10, Issue 2, Pages 51–134 (Mi fpm765)  

This article is cited in 8 scientific papers (total in 8 papers)

Elementary equivalence of categories of modules over rings, endomorphism rings, and automorphism groups of modules

E. I. Bunina, A. V. Mikhalev

M. V. Lomonosov Moscow State University

Abstract: In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of submodules of modules, and automorphism groups of modules.

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English version:
Journal of Mathematical Sciences (New York), 2006, 137:6, 5275–5335

Bibliographic databases:

UDC: 510.67+512.55+512.58

Citation: E. I. Bunina, A. V. Mikhalev, “Elementary equivalence of categories of modules over rings, endomorphism rings, and automorphism groups of modules”, Fundam. Prikl. Mat., 10:2 (2004), 51–134; J. Math. Sci., 137:6 (2006), 5275–5335

Citation in format AMSBIB
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\by E.~I.~Bunina, A.~V.~Mikhalev
\paper Elementary equivalence of categories of modules over rings, endomorphism rings, and automorphism groups of modules
\jour Fundam. Prikl. Mat.
\yr 2004
\vol 10
\issue 2
\pages 51--134
\mathnet{http://mi.mathnet.ru/fpm765}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2113045}
\zmath{https://zbmath.org/?q=an:1073.20045}
\elib{http://elibrary.ru/item.asp?id=9068304}
\transl
\jour J. Math. Sci.
\yr 2006
\vol 137
\issue 6
\pages 5275--5335
\crossref{https://doi.org/10.1007/s10958-006-0297-1}
\elib{http://elibrary.ru/item.asp?id=14220996}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747111702}


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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. E. I. Bunina, A. V. Mikhalev, “Elementary equivalence of endomorphism rings of Abelian $p$-groups”, J. Math. Sci., 137:6 (2006), 5212–5274  mathnet  crossref  mathscinet  zmath  elib  elib
    2. E. I. Bunina, A. V. Mikhalev, “Elementary properties of categories of acts over monoids”, Algebra and Logic, 45:6 (2006), 389–402  mathnet  crossref  mathscinet  zmath  elib  elib
    3. E. I. Bunina, M. A. Roizner, “Elementary equivalence of the automorphism groups of Abelian $p$-groups”, J. Math. Sci., 169:5 (2010), 614–635  mathnet  crossref  mathscinet  elib  elib
    4. M. A. Roizner, “A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, J. Math. Sci., 193:4 (2013), 586–590  mathnet  crossref
    5. M. A. Roizner, “A criterion of elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, J. Math. Sci., 201:4 (2014), 519–526  mathnet  crossref  mathscinet
    6. M. A. Roizner, “Elementary equivalence of automorphism groups of reduced Abelian $p$-groups”, Moscow University Mathematics Bulletin, 68:3 (2013), 156–161  mathnet  crossref  mathscinet
    7. E. I. Bunina, A. V. Mikhalev, I. O. Solovyev, “Elementary equivalence of stable linear groups over local commutative rings with $1/2$”, J. Math. Sci., 233:5 (2018), 646–655  mathnet  crossref
    8. E. I. Bunina, N. V. Yugai, “Elementarnaya ekvivalentnost monoidov endomorfizmov pochti svobodnykh poligonov”, Fundament. i prikl. matem., 21:2 (2016), 37–52  mathnet
  • Фундаментальная и прикладная математика
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