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This article is cited in 3 scientific papers (total in 3 papers)
Universal geometrical equivalence of the algebraic structures of common signature
E. Yu. Daniyarovaa, A. G. Myasnikovb, V. N. Remeslennikova a Sobolev Institute of Mathematics, Omsk Branch, Omsk, Russia
b School of Engineering & Science, Stevens Institute of Technology, Hoboken NJ, USA
Abstract:
This article is a part of our effort to explain the foundations of algebraic geometry over arbitrary algebraic structures [1–8]. We introduce the concept of universal geometrical equivalence of two algebraic structures $\mathscr A$ and $\mathscr B$ of a common language {\tt L} which strengthens the available concept of geometrical equivalence and expresses the maximal affinity between $\mathscr A$ and $\mathscr B$ from the viewpoint of their algebraic geometries. We establish a connection between universal geometrical equivalence and universal equivalence in the sense of equality of universal theories.
Keywords:
universal algebraic geometry, algebraic structure, universal geometrical equivalence, universal equivalence, universal class.
Received: 09.06.2017
Citation:
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Universal geometrical equivalence of the algebraic structures of common signature”, Sibirsk. Mat. Zh., 58:5 (2017), 1035–1050; Siberian Math. J., 58:5 (2017), 801–812
Linking options:
https://www.mathnet.ru/eng/smj2917 https://www.mathnet.ru/eng/smj/v58/i5/p1035
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Abstract page: | 261 | Full-text PDF : | 180 | References: | 44 | First page: | 7 |
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