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Punctual Dimension of Algebraic Structures in Certain Classes

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Abstract

Punctual presentations of algebraic structures in several familiar classes are studied. It is proved that the punctual dimension of punctual structures from the following classes is either 1 or \(\infty\): equivalence structures, linear orders, torsion-free abelian groups, abelian \(p\)-groups, Boolean algebras.

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ACKNOWLEDGMENTS

This work was done during The First Workshop at the Mathematical Center in Akademgorodok (website of the workshop: http://mca.nsu.ru/workshopen/). The authors would like to thank the organizers of the workshop, and are immensely thankful to the project mentors Nikolay Bazhenov and Alexander Melnikov for their valuable guidance.

Funding

A. Issakhov was supported by the Ministry of Education and Science of the Republic of Kazakhstan, grant AP08856834 ‘‘Problems on Rogers semilattices of families of sets in the first and second levels of the Ershov hierarchy’’. B. Kalmurzayev was supported by the Ministry of Education and Science of the Republic of Kazakhstan, grant AP08856493 ‘‘Positive graphs and computable reducibility on them as mathematical model of databases’’. R. Kornev was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1675 with the Ministry of Science and Higher Education of the Russian Federation. M. Kotov was supported by Mathematical Center in Akademgorodok, the agreement with Ministry of Science and High Education of the Russian Federation number 075-15-2019-1613.

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Authors and Affiliations

  1. Massey University, 0745, Auckland, New Zealand

    M. V. Dorzhieva

  2. Kazakh-British Technical University, 050000, Alma-Ata, Kazakhstan

    A. A. Issakhov & B. S. Kalmurzayev

  3. al-Farabi Kazakh National University, 050040, Almaty, Republic of Kazakhstan

    B. S. Kalmurzayev

  4. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia

    R. A. Kornev

  5. Sobolev Institute of Mathematics (Omsk Branch), 644043, Omsk, Russia

    M. V. Kotov

Authors
  1. M. V. Dorzhieva
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  2. A. A. Issakhov
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  3. B. S. Kalmurzayev
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  4. R. A. Kornev
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  5. M. V. Kotov
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Corresponding authors

Correspondence to M. V. Dorzhieva, A. A. Issakhov, B. S. Kalmurzayev, R. A. Kornev or M. V. Kotov.

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(Submitted by A. G. Melnikov)

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Dorzhieva, M.V., Issakhov, A.A., Kalmurzayev, B.S. et al. Punctual Dimension of Algebraic Structures in Certain Classes. Lobachevskii J Math 42, 716–725 (2021). https://doi.org/10.1134/S1995080221040089

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  • DOI: https://doi.org/10.1134/S1995080221040089

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