Enviar artigo por via de e-mail Universal equivalence of general linear groups over local rings with 1/2
- Autores: Kaleeva G.A.1
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Afiliações:
- Lomonosov Moscow State University, Moscow, Russia
- Edição: Volume 216, Nº 10 (2025)
- Páginas: 29-41
- Seção: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/331244
- DOI: https://doi.org/10.4213/sm9695
- ID: 331244
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Resumo
It is proved that the universal equivalence of full 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 and the universal equivalence of the respective rings or the universal equivalence of one ring to the ring opposite to the other.
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Sobre autores
Galina Kaleeva
Lomonosov Moscow State University, Moscow, Russia
Email: galinakaleeva@yandex.ru
without scientific degree, no status
Bibliografia
- C. I. Beidar, A. V. Michalev, “On Malcev's theorem on elementary equivalence of linear groups”, Proceedings of the international conference on algebra, Part 1 (Novosibirsk, 1989), Contemp. Math., 131, Part 1, Amer. Math. Soc., Providence, RI, 1992, 29–35
- D. Segal, K. Tent, “Defining $R$ and $G(R)$”, J. Eur. Math. Soc. (JEMS), 25:8 (2023), 3325–3358
- N. Avni, A. Lubotsky, C. Meiri, “First order rigidity of non-uniform higher rank arithmetic groups”, Invent. Math., 217:1 (2019), 219–240
- A. G. Myasnikov, M. Sohrabi, Bi-interpretability with $mathbb{Z}$ and models of the complete elementary theories of $operatorname{SL}_n(O)$, $mathrm T_n(O)$ and $operatorname{GL}_n(O)$, $n geq 3$
- T. Y. Lam, A first course in noncommutative rings, Grad. Texts in Math., 131, Springer-Verlag, New York, 1991, xvi+397 pp.
- T. Y. Lam, Lectures on modules and rings, Grad. Texts in Math., 189, Springer-Verlag, New York, 1998, xxiv+557 pp.
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