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Fundam. Prikl. Mat., 2019, Volume 22, Issue 4, Pages 75–100 (Mi fpm1817)  

Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures

E. Yu. Daniyarovaa, A. G. Myasnikovb, V. N. Remeslennikova

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
b Stevens Institute of Technology

Abstract: This paper belongs to our series of works on algebraic geometry over arbitrary algebraic structures. In this one, there will be investigated seven equivalences (namely: geometrical, universal geometrical, quasi-equational, universal, elementary, and combinations thereof) in specific classes of algebraic structures (equationally Noetherian, $\mathrm{q}_\omega$-compact, $\mathrm{u}_\omega$-compact, equational domains, equational co-domains, etc.). The main questions are the following: (1) Which equivalences coincide inside a given class $\mathbf K$, which do not? (2) With respect to which equivalences a given class $\mathbf K$ is invariant, with respect to which it is not?

Funding Agency Grant Number
Russian Science Foundation 17-11-01117


Full text: PDF file (342 kB)
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UDC: 510.67+512.71

Citation: E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures”, Fundam. Prikl. Mat., 22:4 (2019), 75–100

Citation in format AMSBIB
\Bibitem{DanMyaRem19}
\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures
\jour Fundam. Prikl. Mat.
\yr 2019
\vol 22
\issue 4
\pages 75--100
\mathnet{http://mi.mathnet.ru/fpm1817}


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  • Фундаментальная и прикладная математика
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