E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. II. Foundations”, Fundam. Prikl. Mat., 17:1 (2012), 65–106; J. Math. Sci., 185:3 (2012), 389

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Fundamentalnaya i Prikladnaya Matematika, 2012, Volume 17, Issue 1, Pages 65–106 (Mi fpm1390)

This article is cited in 47 scientific papers (total in 47 papers)

Algebraic geometry over algebraic structures. II. Foundations

E. Yu. Daniyarova^a, A. G. Myasnikov^b, V. N. Remeslennikov^a

^a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
^b Stevens Institute of Technology, USA

Full-text PDF (382 kB) Citations (47)

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Abstract: In this paper, we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove so-called unification theorems which describe coordinate algebras of algebraic sets in several different ways.

English version:
Journal of Mathematical Sciences (New York), 2012, Volume 185, Issue 3, Pages 389–416
DOI: https://doi.org/10.1007/s10958-012-0923-z

Bibliographic databases:

Document Type: Article

UDC: 512.57+512.7

Language: Russian

Citation: E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. II. Foundations”, Fundam. Prikl. Mat., 17:1 (2012), 65–106; J. Math. Sci., 185:3 (2012), 389–416

Citation in format AMSBIB

\Bibitem{DanMyaRem12}

\by E.~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov

\paper Algebraic geometry over algebraic structures.~II. Foundations

\jour Fundam. Prikl. Mat.

\yr 2012

\vol 17

\issue 1

\pages 65--106

\mathnet{http://mi.mathnet.ru/fpm1390}

\transl

\jour J. Math. Sci.

\yr 2012

\vol 185

\issue 3

\pages 389--416

\crossref{https://doi.org/10.1007/s10958-012-0923-z}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866314545}

Linking options:

https://www.mathnet.ru/eng/fpm1390

https://www.mathnet.ru/eng/fpm/v17/i1/p65

Cycle of papers

Algebraic geometry over algebraic structures. II. Foundations
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov
Fundam. Prikl. Mat., 2012, 17:1, 65–106
Algebraic geometry over algebraic structures. IV. Equational domains and codomains
É Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov
Algebra Logika, 2010, 49:6, 715–756
Algebraic geometry over algebraic structures. V. The case of arbitrary signature
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov
Algebra Logika, 2012, 51:1, 41–60
Algebraic geometry over algebraic structures. VI. Geometric equivalence
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov
Algebra Logika, 2017, 56:4, 421–442
Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov
Algebra Logika, 2018, 57:6, 639–661
Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov
Fundam. Prikl. Mat., 2019, 22:4, 75–100

This publication is cited in the following 47 articles:

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	752
Full-text PDF :	340
References:	96
First page:	1

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