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Akademický článek

Multi-Sorted Logic and Logical Geometry: Some Problems

Autor: Plotkin B., Plotkin E.

Publikováno v: Demonstratio Mathematica, Vol 48, Iss 4, Pp 578-619 (2015)

The paper has a form of a survey on basics of logical geometry and consists of three parts. It is focused on the relationship between many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on important model-theoret

Externí odkaz: https://doaj.org/article/49a430f7b26a43fbb63fb407c6b68698

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Small cancelation rings

Autor: Atkarskaya, A., Kanel-Belov, A., Plotkin, E., Rips, E.

Publikováno v: Mathematics Research Reports, 2 (2021), 1-14

The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining relations. The rel

Externí odkaz: http://arxiv.org/abs/2010.03992

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Group-like small cancellation theory for rings

Autor: Atkarskaya, A., Kanel-Belov, A., Plotkin, E., Rips, E.

Publikováno v: International Journal of Algebra and Computation, 33:07 (2023).1269-1487

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding defining relation

Externí odkaz: http://arxiv.org/abs/2010.02836

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Construction of a quotient ring of $\mathbb{Z}_2\mathcal{F}$ in which a binomial $1 + w$ is invertible using small cancellation methods

Autor: Atkarskaya, A., Kanel-Belov, A., Plotkin, E., Rips, E.

We apply small cancellation methods originating from group theory to investigate the structure of a quotient ring $\mathbb{Z}_2\mathcal{F} / \mathcal{I}$, where $\mathbb{Z}_2\mathcal{F}$ is the group algebra of the free group $\mathcal{F}$ over the f

Externí odkaz: http://arxiv.org/abs/1807.10070

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Thompson-like characterization of the solvable radical

Autor: Guralnick, R., Kunyavskii, B., Plotkin, E., Shalev, A.

Publikováno v: J. Algebra 300 (2006), 363-375

We prove that the solvable radical of a finite group G coincides with the set of elements y having the following property: for any x in G the subgroup of G generated by x and y is solvable. We present analogues of this result for finite dimensional L

Externí odkaz: http://arxiv.org/abs/math/0504176

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