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Algebra Logika, 2010, Volume 49, Number 6, Pages 715–756 (Mi al464)  

This article is cited in 24 scientific papers (total in 24 papers)

Algebraic geometry over algebraic structures. IV. Equational domains and codomains

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

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk, Russia
b Schaefer School of Engineering and Science, Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, USA

Abstract: We introduce and study equational domains and equational codomains. Informally, an equational domain is an algebra every finite union of algebraic sets over which is an algebraic set; an equational codomain is an algebra every proper finite union of algebraic sets over which is not an algebraic set.

Keywords: algebra, algebraic set, universal algebraic geometry, disjunctive equation, equational domain, equational codomain, discriminating algebra, codiscriminating algebra.

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English version:
Algebra and Logic, 2010, 49:6, 483–508

Bibliographic databases:

UDC: 512.71+512.577+512.55
Received: 07.08.2010
Revised: 28.11.2010

Citation: É Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. IV. Equational domains and codomains”, Algebra Logika, 49:6 (2010), 715–756; Algebra and Logic, 49:6 (2010), 483–508

Citation in format AMSBIB
\by \'E~Yu.~Daniyarova, A.~G.~Myasnikov, V.~N.~Remeslennikov
\paper Algebraic geometry over algebraic structures.~IV. Equational domains and codomains
\jour Algebra Logika
\yr 2010
\vol 49
\issue 6
\pages 715--756
\jour Algebra and Logic
\yr 2010
\vol 49
\issue 6
\pages 483--508

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    2. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. V. The case of arbitrary signature”, Algebra and Logic, 51:1 (2012), 28–40  mathnet  crossref  mathscinet  zmath  isi
    3. Plotkin B., Aladova E., Plotkin E., “Algebraic Logic and Logically-Geometric Types in Varieties of Algebras”, J. Algebra. Appl., 12:2 (2013), 1250146  crossref  mathscinet  zmath  isi  elib  scopus
    4. M. V. Kotov, “Topologizability of countable equationally Noetherian algebras”, Algebra and Logic, 52:2 (2013), 105–115  mathnet  crossref  mathscinet  isi
    5. 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
    6. A. N. Shevlyakov, “Equations over completely simple semigroups”, Algebra and Logic, 53:6 (2015), 520–524  mathnet  crossref  mathscinet  isi
    7. 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  scopus
    8. A. G. Pinus, “On the quasiorder induced by inner homomorphisms and the operator of algebraic closure”, Siberian Math. J., 56:3 (2015), 499–504  mathnet  crossref  crossref  mathscinet  isi  elib  elib
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    10. 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
    11. P. Modabberi, M. Shahryari, “Equational conditions in universal algebraic geometry”, Algebra and Logic, 55:2 (2016), 146–172  mathnet  crossref  crossref  isi
    12. P. Modabberi, M. Shahryari, “On the equational Artinian algebras”, Sib. elektron. matem. izv., 13 (2016), 875–881  mathnet  crossref
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    14. A. G. Pinus, “Algebraically equivalent clones”, Algebra and Logic, 55:6 (2017), 501–506  mathnet  crossref  crossref  isi
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    16. Khodabandeh H., Shahryari M., “Equations in Polyadic Groups”, Commun. Algebr., 45:3 (2017), 1227–1238  crossref  mathscinet  zmath  isi  scopus
    17. Shevlyakov A.N., “on Disjunctions of Algebraic Sets in Completely Simple Semigroups”, Commun. Algebr., 45:9 (2017), 3757–3767  crossref  mathscinet  zmath  isi  scopus
    18. 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
    19. Shahryari M., “Algebraic Sets With Fully Characteristic Radicals”, J. Sib. Fed. Univ.-Math. Phys., 10:3 (2017), 293–297  mathnet  crossref  mathscinet  isi  scopus
    20. 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
    21. 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
    22. 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
    23. Di Nola A., Lenzi G., Vitale G., “Algebraic Geometry For l-Groups”, Algebr. Universalis, 79:3 (2018), UNSP 64  crossref  mathscinet  isi  scopus
    24. Nikitin A.Yu., Kudyk I.D., Mechanical Science and Technology Update (Mstu-2018), Journal of Physics Conference Series, 1050, IOP Publishing Ltd, 2018  crossref  isi  scopus
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