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Fundam. Prikl. Mat., 2012, Volume 17, Issue 1, Pages 65–106 (Mi fpm1390)  

This article is cited in 26 scientific papers (total in 26 papers)

Algebraic geometry over algebraic structures. II. Foundations

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

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

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.

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English version:
Journal of Mathematical Sciences (New York), 2012, 185:3, 389–416

UDC: 512.57+512.7

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
\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
\jour J. Math. Sci.
\yr 2012
\vol 185
\issue 3
\pages 389--416

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    10. P. Modabberi, M. Shahryari, “Equational conditions in universal algebraic geometry”, Algebra and Logic, 55:2 (2016), 146–172  mathnet  crossref  crossref  isi
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    19. A. G. Pinus, “Algebraic sets of universal algebras and algebraic closure operator”, Lobachevskii J. Math., 38:4, SI (2017), 719–723  crossref  mathscinet  zmath  isi  scopus
    20. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic Geometry Over Algebraic Structures. IX. Principal Universal Classes and Dis-Limits”, Algebra and Logic, 57:6 (2019), 414–428  mathnet  crossref  crossref  isi
    21. Daniyarova Evelina Yur'evna Myasnikov A.G. Remeslennikov V.N., “Algebraic Geometry Over Algebraic Structures X: Ordinal Dimension”, Int. J. Algebr. Comput., 28:8, SI (2018), 1425–1448  crossref  mathscinet  zmath  isi  scopus
    22. Serdyukova N., Serdyukov V., “Formalization of System Links: Different Approaches. Duality in Smart Systems Theory”: Serdyukova, N Serdyukov, V, Algebraic Formalization of Smart Systems: Theory and Practice, Smart Innovation Systems and Technologies, 91, Springer-Verlag Berlin, 2018, 79–96  crossref  isi  scopus
    23. A. A. Mischenko, V. N. Remeslennikov, A. V. Treier, “Kanonicheskie i algebraicheski zamknutye gruppy v universalnykh klassakh abelevykh grupp”, Algebra i logika, 58:3 (2019), 344–362  mathnet  crossref
    24. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraicheskaya geometriya nad algebraicheskimi sistemami. VIII. Geometricheskie ekvivalentnosti i osobye klassy algebraicheskikh sistem”, Fundament. i prikl. matem., 22:4 (2019), 75–100  mathnet
    25. Mahdiyeh Nouri, “Algebraic geometry over Heyting algebras”, Zhurn. SFU. Ser. Matem. i fiz., 13:4 (2020), 414–421  mathnet  crossref
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  • Фундаментальная и прикладная математика
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