Algebra and Logic

, Volume 58, Issue 4, pp 313–321 | Cite as

Universal Equivalence of Linear Groups Over Local Commutative Rings with 1/2

  • G. A. KaleevaEmail author

It is proved that the universal equivalence of general or special linear groups of orders greater than 2 over local commutative rings with 1/2 is equivalent to the coincidence of orders of groups and universal equivalence of respective rings.


universal equivalence general linear groups special linear groups local rings 


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  1. 1.
    E. I. Bunina and G. A. Kaleeva, “Universal equivalence of general and special linear groups over fields,” Fund. Prikl. Mat., 21, No. 3, 73-106 (2016).MathSciNetzbMATHGoogle Scholar
  2. 2.
    A. I. Mal’tsev, “Elementary properties of linear groups,” in Some Problems in Mathematics and Mechanics [in Russian], SO AN SSSR, Novosibirsk (1961), pp. 110-132.Google Scholar
  3. 3.
    M. F. Atiyah and I. G. MacDonald, Introduction to Commutative Algebra, Addison Wesley (1969).Google Scholar
  4. 4.
    I. Z. Golubchik and A. V. Mikhalev, “Isomorphisms of the general linear group over an associative ring,” Vest. MGU, Ser. 1, Mat., Mekh., No. 3, 61-72 (1983).Google Scholar
  5. 5.
    J. Pomfret and B. R. McDonald, “Automorphisms of GLn, R a local ring,” Trans. Am. Math. Soc., 173, 379-388 (1972).zbMATHGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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