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

This article is cited in 22 scientific papers (total in 22 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
\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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866314545}


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    This publication is cited in the following articles:
    1. M. G. Amaglobeli, V. N. Remeslennikov, “Rasshirenie tsentralizatora v nilpotentnykh gruppakh”, Sib. matem. zhurn., 54:1 (2013), 8–19  mathnet  mathscinet
    2. A. N. Shevlyakov, “Algebraic geometry over Boolean algebras in the language with constants”, J. Math. Sci., 206:6 (2015), 742–757  mathnet  crossref  mathscinet
    3. A. N. Shevlyakov, “Unifying solutions to systems of equations in finite simple semigroups”, Algebra and Logic, 53:1 (2014), 70–83  mathnet  crossref  mathscinet  isi
    4. A. N. Shevlyakov, “Equations over completely simple semigroups”, Algebra and Logic, 53:6 (2015), 520–524  mathnet  crossref  mathscinet  isi
    5. Daniyarova E.Yu., Myasnikov A.G., Remeslennikov V.N., “Dimension in Universal Algebraic Geometry”, Dokl. Math., 90:1 (2014), 450–452  crossref  mathscinet  zmath  isi  elib
    6. A. N. Shevlyakov, “Elements of algebraic geometry over a free semilattice”, Algebra and Logic, 54:3 (2015), 258–271  mathnet  crossref  crossref  mathscinet  isi
    7. A. G. Pinus, “Algebras with identical algebraic sets”, Algebra and Logic, 54:4 (2015), 316–322  mathnet  crossref  crossref  mathscinet  isi
    8. A. N. Shevlyakov, “Combining solutions for systems equations in semigroups with finite ideal”, Algebra and Logic, 55:1 (2016), 58–71  mathnet  crossref  crossref  isi  elib
    9. A. N. Shevlyakov, “Ekvivalentnye uravneniya nad polureshetkami”, Sib. elektron. matem. izv., 13 (2016), 478–490  mathnet  crossref
    10. P. Modabberi, M. Shahryari, “Equational conditions in universal algebraic geometry”, Algebra and Logic, 55:2 (2016), 146–172  mathnet  crossref  crossref  isi
    11. P. Modabberi, M. Shahryari, “On the equational Artinian algebras”, Sib. elektron. matem. izv., 13 (2016), 875–881  mathnet  crossref
    12. A. N. Shevlyakov, “Universal algebraic geometry with relation $\not=$”, Algebra and Logic, 55:4 (2016), 330–339  mathnet  crossref  crossref  isi
    13. P. A. Ulyashev, “Algebraic geometry over completely simple semigroups”, Algebra and Logic, 55:5 (2016), 394–402  mathnet  crossref  crossref  isi
    14. M. A. Vakhrameev, “Sluchainye uravneniya nad svobodnymi polureshetkami”, PDM, 2017, no. 36, 5–12  mathnet  crossref
    15. Mohammad Shahryari, “Algebraic sets with fully characteristic radicals”, Zhurn. SFU. Ser. Matem. i fiz., 10:3 (2017), 293–297  mathnet  crossref
    16. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VI. Geometric equivalence”, Algebra and Logic, 56:4 (2017), 281–294  mathnet  crossref  crossref  isi
    17. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Universal geometrical equivalence of the algebraic structures of common signature”, Siberian Math. J., 58:5 (2017), 801–812  mathnet  crossref  crossref  isi  elib  elib
    18. M. Shahryari, A. Shevlyakov, “Direct products, varieties, and compactness conditions”, Groups Complex. Cryptol., 9:2 (2017), 159–166  crossref  mathscinet  zmath  isi  scopus
    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
  • Фундаментальная и прикладная математика
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