Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence

E. Yu Daniyarova; A. G. Myasnikov; V. N. Remeslennikov

doi:10.1007/s10469-017-9449-2

Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence

E. Yu Daniyarova, A. G. Myasnikov, V. N. Remeslennikov

Department of Mathematical Sciences

RAS - Sobolev Institute of Mathematics, Siberian Branch

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

The present paper is one in our series of works on algebraic geometry over arbitrary algebraic structures, which focuses on the concept of geometrical equivalence. This concept signifies that for two geometrically equivalent algebraic structures A and ℬ of a language L, the classification problems for algebraic sets over A and ℬ are equivalent. We establish a connection between geometrical equivalence and quasiequational equivalence.

Original language	English
Pages (from-to)	281-294
Number of pages	14
Journal	Algebra and Logic
Volume	56
Issue number	4
DOIs	https://doi.org/10.1007/s10469-017-9449-2
State	Published - 1 Sep 2017

Keywords

algebraic structure
geometrical equivalence
prevariety
quasivariety
universal algebraic geometry

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KW - quasivariety

KW - universal algebraic geometry

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Algebraic Geometry Over Algebraic Structures. VI. Geometrical Equivalence

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Keywords

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