Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Solomatin D. V. Planarity ranks for varieties of equationally noetherian semigroups. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2025, vol. 25, iss. 1, pp. 53-56. DOI: 10.18500/1816-9791-2025-25-1-53-56, EDN: JLOWEC

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
28.02.2025
Full text:
download
(downloads: 47)
Language: 
Russian
Heading: 
Mathematics
Article type: 
Short communication
UDC: 
512.572
DOI: 
10.18500/1816-9791-2025-25-1-53-56
EDN: 
JLOWEC

Planarity ranks for varieties of equationally noetherian semigroups

Autors: 
Solomatin Denis Vladimirovich, Omsk State Pedagogical University
Abstract: 

The problem of describing semigroup varieties with finite planarity rank is researched. In addition to the previously obtained results the author finds new countable infinite series of semigroup varieties with finite planarity rank.

Key words: 
semigroup
Cayley graph of a semigroup
planar graph
nontrivial semigroup identity
Acknowledgments: 
The author is grateful to Professor A. N. Shevlyakov for kindly providing additional materials on varieties of Noetherian semigroups by equations and constructive remarks.
References: 
  1. Korshunov A. D. The main properties of random graphs with a large number of vertices and edges. Russian Mathematical Surveys, 1985, vol. 40, iss. 1, pp. 121–198. https://doi.org/10.1070/RM1985v040n01ABEH003529
  2. Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I. Lectures on graph theory. Moscow, Nauka, 1990. 384 p. (in Russian).
  3. Shevlyakov A. N. Direct powers of algebraic structures and equations. Applied Discrete Mathematics, 2022, iss. 58, pp. 31–39. https://doi.org/10.17223/20710410/58/4, EDN: SLWROD
  4. Solomatin D. V. Planarity ranks of the varieties of commutative monoids. Herald of Omsk University, 2012, iss. 4 (66), pp. 41–45 (in Russian). EDN: RRQLSF
  5. Solomatin D. V. The ranks of planarity for varieties of commutative semigroups. Applied Discrete Mathematics, 2016, iss. 4 (34), pp. 50–64. (in Russian). https://doi.org/10.17223/20710410/34/4, EDN: XEAAEX
  6. Solomatin D. V. Planar varieties of semigroups. Siberian Electronic Mathematical Reports, 2015, vol. 12, pp. 232–247 (in Russian). https://doi.org/10.17377/semi.2015.12.019, EDN: VKASBJ
Received: 
19.12.2023
Accepted: 
13.03.2024
Published: 
28.02.2025
  • 120 reads