Elementary equivalence and isomorphisms of locally nilpotent matrix groups and rings

被引：2

作者：

Levchuk, V. M. ^{[1
]}

Minakova, E. V. ^{[1
]}

机构：

[1] Siberian Fed Univ, Inst Math, Dept Algebra & Math Log, Krasnoyarsk 660041, Russia

来源：

DOKLADY MATHEMATICS | 2009年 / 79卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

ALGEBRA;

D O I：

10.1134/S1064562409020100

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Elementary equivalence and isomorphisms of locally nilpotent matrix groups and rings was reported. A fundamental correspondence between the elementary properties of the unitriangular group of degree 3 and the coefficient ring was detected. The relationship between ring derivations and endomorphisms is revealed by various lemma. The various theorems reveal a relationship between the elementary equivalence of the associated rings with the elementary properties of the base rings. Derivations in a ring are trivial Lie and Jordan derivations, and isomorphisms and anti-isomorphisms between rings are trivial Jordan isomorphisms. The elementary equivalence of coefficient rings can be easily transferred to uni triangular groups of the same degree and to the associated Lie and Jordan rings.

引用

页码：185 / 188

页数：4

共 15 条

[1] BELEGRADEK OV, 1999, AM MATH SOC T, V195
[2] CHANG CC, 1977, MODEL THEORY
[3] Herstein I. N., 1957, Proc. Amer. Math. Soc., V8, P1104, DOI [10.2307/2032688, 10.1090/S0002-9939-1957-0095864-2, DOI 10.1090/S0002-9939-1957-0095864-2]
[4] Herstein IN., 1956, Trans. Am. Math. Soc, V81, P331, DOI [10.1090/S0002-9947-1956-0076751-6, DOI 10.1090/S0002-9947-1956-0076751-6]
[5] Isomorphisms of certain locally nilpotent finitary groups and associated rings
Kuzucuoglu, F
Levchuk, VM
[J]. ACTA APPLICANDAE MATHEMATICAE, 2004, 82 (02) : 169 - 181
[6] LEVCHUK VM, 1983, SIBERIAN MATH J+, V24, P543
[7] LEVCHUK VM, 1987, MAT ZAMETKI, V42, P631
[8] LEVCHUK VM, 1975, DOKL AKAD NAUK SSSR, V16, P756
[9] Mal'cev A.I., 1960, MAT SOBRONIK, V50, P257
[10] MINAKOVA EV, 2008, VESTN NOVOSIBIRSK U, V8, P100

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