E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. V. The case of arbitrary signature”, Algebra Logika, 51:1 (2012), 41–60; Algebra and Logic, 51:1 (2012), 28

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Algebra i logika, 2012, Volume 51, Number 1, Pages 41–60 (Mi al521)

This article is cited in 25 scientific papers (total in 25 papers)

Algebraic geometry over algebraic structures. V. The case of arbitrary signature

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 Sciences, Omsk, Russia
^b Schaefer School of Engineering and Science, Dep. of Math. Sci., Stevens Institute of Technology, Hoboken, NJ, USA

Full-text PDF (231 kB) Citations (25)

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Abstract: A general theory of algebraic geometry over an arbitrary algebraic structure

A

$\mathcal A$ in a language

L

$\mathrm L$ with no predicates is consistently presented in a series of papers on universal algebraic geometry [B. Fine (ed.) et al., Aspects of infinite groups. A Festschrift in honor of A. Gaglione (Papers of the conf., Fairfield, USA, March 2007 in honour of A. Gaglione's 60th birthday), (Algebra Discr. Math. (Hackensack), 1), Hackensack, NJ, World Sci., 2008, 80–111; submitted to Fund. Appl. Math.; Southeast Asian Bull. Math., accepted for publ.; Algebra i Logika, 49, No. 6 (2010), 715–756]. The restriction that we impose on the language is not crucial. This is done for the sake of readers who only get acquainted with universal algebraic geometry. Here we show how the entire material accumulated in works on universal geometry can be carried over without essential changes to the case of an arbitrary signature

L

$\mathrm L$ .

Keywords: universal algebraic geometry, algebraic structure, algebraic set, coordinate algebra.

Received: 23.05.2011

English version:
Algebra and Logic, 2012, Volume 51, Issue 1, Pages 28–40
DOI: https://doi.org/10.1007/s10469-012-9168-7

Bibliographic databases:

Document Type: Article

UDC: 510.67+512.71

Language: Russian

Citation: E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. V. The case of arbitrary signature”, Algebra Logika, 51:1 (2012), 41–60; Algebra and Logic, 51:1 (2012), 28–40

Citation in format AMSBIB

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\jour Algebra and Logic

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Linking options:

https://www.mathnet.ru/eng/al521

https://www.mathnet.ru/eng/al/v51/i1/p41

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 25 articles:

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Jiansong Zhang, Fan Yang, Digital Twins in Construction and the Built Environment, 2024, 37
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Pasha Zusmanovich, “On the utility of Robinson–Amitsur ultrafilters. III”, Period Math Hung, 85:2 (2022), 399
Wu J., Sadraddin H.L., Ren R., Zhang J., Shao X., “Invariant Signatures of Architecture, Engineering, and Construction Objects to Support Bim Interoperability Between Architectural Design and Structural Analysis”, J. Constr. Eng. Manage., 147:1 (2021), 04020148
Tsurkov A., “Automorphic Equivalence in the Varieties of Representations of Lie Algebras”, Commun. Algebr., 48:1 (2020), 397–409
J. Simões da Silva, A. Tsurkov, “Geometrical equivalence and action type geometrical equivalence of group representations”, Algebra Discrete Math., 30:2 (2020), 273–281
A Yu Nikitin, A N Shevlyakov, “On radicals of system of equations over linear strict posets”, J. Phys.: Conf. Ser., 1441:1 (2020), 012156
Wu J., Zhang J., “Introducing Geometric Signatures of Architecture, Engineering, and Construction Objects and a New Bim Dataset”, Computing in Civil Engineering 2019: Visualization, Information Modeling, and Simulation, eds. Cho Y., Leite F., Behzadan A., Wang C., Amer Soc Civil Engineers, 2019, 264–271
Nikitin A.Yu., Xii International Scientific and Technical Conference Applied Mechanics and Systems Dynamics, Journal of Physics Conference Series, 1210, IOP Publishing Ltd, 2019
E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. VIII. Geometric equivalences and special classes of algebraic structures”, J. Math. Sci., 257:6 (2021), 797–813
Jin Wu, Jiansong Zhang, Computing in Civil Engineering 2019, 2019, 264
A Yu Nikitin, “On radicals and coordinate partial orders”, J. Phys.: Conf. Ser., 1260:2 (2019), 022004
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
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
Nikitin A.Yu., Kudyk I.D., Mechanical Science and Technology Update (Mstu-2018), Journal of Physics Conference Series, 1050, IOP Publishing Ltd, 2018
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
A. Tsurkov, “Automorphic equivalence in the classical varieties of linear algebras”, Int. J. Algebr. Comput., 27:8 (2017), 973–999
A. G. Pinus, “Algebraic sets of universal algebras and algebraic closure operator”, Lobachevskii J. Math., 38:4, SI (2017), 719–723
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

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

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