Universal equivalence of general linear groups over local rings with $1/2$

G. A. Kaleeva

Lomonosov Moscow State University, Moscow, Russia

Abstract: It is proved that the universal equivalence of general linear groups of order strictly greater than $2$ over local, not necessarily commutative rings with $1/2$ is equivalent to the coincidence of their orders in combination with the universal equivalence of the respective rings or the universal equivalence of one ring to the ring opposite to the other.
Bibliography: 15 titles.

Keywords: universal equivalence, general linear groups, noncommutative local rings.

MSC: Primary 03C60; Secondary 20H25

Received: 23.11.2021 and 05.12.2024

DOI: 10.4213/sm9695

 English version: Sbornik: Mathematics, 2025, 216:10, 1363–1374

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