The elementary equivalence of Lie rings of niltriangular matrix rings over the commutative rings of coefficients
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 3, pp. 100-104 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the elementary equivalence of Lie rings of niltriangular matrix rings over associative and commutative rings is transferred onto the rings of coefficients.
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E. V. Minakova. The elementary equivalence of Lie rings of niltriangular matrix rings over the commutative rings of coefficients. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 3, pp. 100-104. http://geodesic.mathdoc.fr/item/VNGU_2008_8_3_a5/

[1] Rose B. I., “The $\chi_1-$categoricity of Strictly Upper Triangular Matrix Rings over Algebraically Closed Fields”, J. of Symbolic Logic, 43:2 (1978), 250–259 | DOI | MR | Zbl

[2] Wheeler W. H., “Model Theory of Strictly Upper Triangular Matrix Ring”, J. Symbolic Logic, 45 (1980), 455–463 | DOI | MR | Zbl

[3] Levchuk V. M., “Svyazi unitreugolnoi gruppy s nekotorymi koltsami. II: Gruppy avtomorfizmov”, Sib. mat. zhurn., 24:4 (1983), 543–557 | Zbl

[4] Videla C. R., “On the Model Theory of the Ring $NT(n,R)$”, J. of Pure and Appl. Algebra, 55 (1988), 289–302 | DOI | MR | Zbl

[5] Belegradek O. V., “Model Theory of Unitriangular Groups”, Amer. Math. Soc. Transl., 195:2 (1999) | MR | Zbl

[6] Kuzucuoglu F., Levchuk V. M., “Isomorphisms of Certain Locally Nilpotent Finitary Groups and Associated Rings”, Acta Appl. Math., 82:2 (2004), 169–181 | DOI | MR | Zbl

[7] Levchuk V. M., “Sylow Subgroups of Chevalley Groups and Associated (weakly) Finitary Groups and Rings”, Acta Appl. Math., 85 (2005), 225–232 | DOI | MR | Zbl

[8] Saks Dzh. E., Teoriya nasyschennykh modelei, Mir, M., 1976 | MR

[9] Maltsev A. I., “Ob odnom sootvetstvii mezhdu koltsami i gruppami”, Mat. sb., 50 (1960), 257–266 | MR | Zbl

[10] Levchuk V. M., “Nekotorye lokalno nilpotentnye matrichnye koltsa”, Mat. zametki, 42:5 (1987), 631–641 | MR | Zbl