REFERENCES
E. Artin, Geometric Algebra, Interscience Publishers, New York-London (1957).
R. Baer, Linear Algebra and Projective Geometry, Academic Press (1952).
C. I. Beidar and A. V. Michalev, “On Malcev's theorem on elementary equivalence of linear groups,” Contemp. Math., 131, 29–35 (1992).
A. Borel, R. Carter, C. W. Curtis, N. Iwahori, T. A. Springer and R. Steinberg, Seminar on Algebraic Groups and Related Finite Groups, Springer-Verlag, Berlin-Heidelberg-New York (1970).
E. I. Bunina, “Elementary equivalence of unitary linear groups over fields,” Fund. Prikl. Mat., 4, 1–14 (1998).
E. I. Bunina, “Elementary equivalence of unitary linear groups over rings and skewfields,” Usp. Mat. Nauk, 53, 137–138 (1998).
E. I. Bunina, “Elementary equivalence of Chevalley groups,” In: Abstracts of 7th Math. Readings of Moscow State University [in Russian], Moscow (2000), pp. 120–124.
N. Bourbaki, Groupes et Algébres de Lie, Hermann (1968).
J. P. Serre, Lie Algebras and Lie Groups [Russian translation], Izd. Platon (1997).
C. C. Chang and H. J. Keisler, Model Theory, North-Holland, Amsterdam-London; American Elsevier, New York.
C. Faith, Algebra: Rings, Modules and Categories. I, Springer-Verlag (1973).
I. Z. Golubchik and A. V. Mikhalev, “Isomorphisms of unitary groups over associative rings,” Zap. Nauchn. Sem. Leningr. Otdel. Mat. Inst. Akad. Nauk SSSR, 132, 97–109 (1983).
I. Z. Golubchik and A. V. Mikhalev, “Isomorphisms of the general linear groups over associative rings,” Vestn. MGU, Mat., Mekh., No. 3, 61–72 (1983).
J. Humphreys, Linear Algebraic Groups, Springer-Verlag, New York-Heidelberg-Berlin (1975).
A. I. Mal'cev, Principles of Linear Algebra [in Russian], Gostekhizdat, Moscow (1956).
A. I. Mal'cev, “Constructive algebras. 1,” Usp. Mat. Nauk, 16, No. 3, 3–60 (1961).
A. I. Mal'cev, “On elementary properties of linear groups,” In: Some Problems in Mathematics and Mechanics [in Russian], Novosibirsk (1961), pp. 110–132.
A. I. Mal'cev, Algebraic Systems [in Russian], Nauka, Moscow (1970).
A. V. Mikhalev, “Multiplicative classification of associative rings,” Mat. Sb., 135, No. 177, 177–188 (1988).
P. S. Novikov, Elements of Mathematical Logic [in Russian], Fizmatgiz, Moscow (1959).
M. M. Postnikov, Lectures on Geometry [in Russian], Nauka, Moscow (1982).
R. Steinberg, Lectures on Chevalley Groups, Yale University (1967).
W. Stephenson, “Lattice isomorphisms between modules,” J. London Math. Soc., 1, 177–188 (1969).
W. Stephenson, Characterizations of Rings and Modules by Means of Lattices, Ph.D. Thesis, University of London.
B. L. Van der Waerden, Gruppen von Linearen Transformationen, Berlin (1935).
Rights and permissions
About this article
Cite this article
Bunina, E.I., Mikhalev, A.V. Elementary properties of linear and algebraic groups. Journal of Mathematical Sciences 110, 2595–2659 (2002). https://doi.org/10.1023/A:1015157631442
Issue Date:
DOI: https://doi.org/10.1023/A:1015157631442