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Elementary equivalence of unitary linear groups over rings

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Abstract

We find necessary and sufficient conditions for two unitary linear groups over rings with involution with forms of hyperbolic rank at least 2 to be elementarily equivalent.

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References

  1. C. I. Beidar and A. V. Mikhalev, “On Mal’cev’s theorem on elementary equivalence of linear groups,” Contemp. Math., 131, No. 1, 29–35 (1992).

    MathSciNet  Google Scholar 

  2. E. I. Bunina, “Elementary equivalence of unitary linear groups over rings and fields,” Usp. Mat. Nauk, 53, No. 2, 137–138 (1998).

    MathSciNet  Google Scholar 

  3. C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam, Elsevier, New York (1973).

    MATH  Google Scholar 

  4. C. Faith, Algebra: Rings, Modules and Categories, Springer, Berlin (1973).

    MATH  Google Scholar 

  5. I. Z. Golubchik and A. V. Mikhalev, “Isomorphisms of unitary groups over associative rings,” Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklova, 132, 97–109 (1983).

    MathSciNet  Google Scholar 

  6. A. I. Maltsev, “On elementary properties of linear groups,” in: Problems of Mathematics and Mechanics [in Russian], Novosibirsk (1961), pp. 110–132.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    E. S. Balmasov & E. I. Bunina

Authors
  1. E. S. Balmasov
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  2. E. I. Bunina
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Correspondence to E. S. Balmasov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 14, No. 2, pp. 13–27, 2008.

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Balmasov, E.S., Bunina, E.I. Elementary equivalence of unitary linear groups over rings. J Math Sci 162, 594–604 (2009). https://doi.org/10.1007/s10958-009-9648-z

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  • DOI: https://doi.org/10.1007/s10958-009-9648-z

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