Zobrazeno 1 - 10
of 319
pro vyhledávání: '"MYASNIKOV, ALEXEI"'
Autor:
Myasnikov, Alexei, Nikolaev, Andrey
We solve the first-order classification problem for rings $R$ of polynomials $F[x_1, \ldots,x_n]$ and Laurent polynomials $F[x_1,x_1^{-1}, \ldots,x_n,x_n^{-1}]$ with coefficients in an infinite field $F$ or the ring of integers $\mathbb Z$, that is,
Externí odkaz:
http://arxiv.org/abs/2409.14467
Autor:
Daniyarova, Evelina, Myasnikov, Alexei
We prove that metabelian Baumslag$-$Solitar group $BS(1,k)$, $k>1$, is (strongly) regularly bi-interpretable with the ring of integers $\mathbb{Z}$, and describe in algebraic terms all groups that are elementarily equivalent to $BS(1,k)$.
Externí odkaz:
http://arxiv.org/abs/2407.00642
Autor:
Myasnikov, Alexei G., Sohrabi, Mahmood
In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as $GL_n(F), SL_n(F)$ and $T_n(F)$ over a field $F$ provided $n \geq 3$.
Comment: 36 pages
Comment: 36 pages
Externí odkaz:
http://arxiv.org/abs/2405.14476
Publikováno v:
In Journal of Algebra 15 July 2024 650:219-274
Publikováno v:
"Groups and Model Theory, GAGTA Book 2", edited by Kharlampovich and Sklinos, published in 2021 by de Gruyter
In this paper we initiate a study of first-order rich groups, i.e., groups where the first-order logic has the same power as the weak second order logic. Surprisingly, there are quite a lot of finitely generated rich groups, they are somewhere in bet
Externí odkaz:
http://arxiv.org/abs/2109.13133
Autor:
Sohrabi, Mahmood, Myasnikov, Alexei G.
Let $\mathcal{O}$ be the ring of integers of a number field, and let $n\geq 3$. This paper studies bi-interpretability of the ring of integers $\mathbb{Z}$ with the special linear group $\text{SL}_n(\mathcal{O})$, the general linear group $\text{GL}_
Externí odkaz:
http://arxiv.org/abs/2004.03585
We modify the notion of a Fra\"iss\'e class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit Fra\"iss\'e limits. Furthermore, we redisc
Externí odkaz:
http://arxiv.org/abs/1807.08131
Autor:
Kharlampovich, Olga, Myasnikov, Alexei
In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb{Z}$ is interpretable by positive existential formulas in such free Li
Externí odkaz:
http://arxiv.org/abs/1708.07419
Autor:
Kharlampovich, Olga, Myasnikov, Alexei
Let $R$ be a commutative integral unital domain and $L$ a free non-commutative Lie algebra over $R$. In this paper we show that the ring $R$ and its action on $L$ are 0-interpretable in $L$, viewed as a ring with the standard ring language $+, \cdot,
Externí odkaz:
http://arxiv.org/abs/1704.07853