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PreprintCC BY-NC-ND 4.0arXiv

On certain classes of commutative g-dimonoids

  • Volodymyr Gavrylkiv
  • Inna Hlushak
  • Kateryna Koporkh
  • Natalia Mazurenko
  • Oksana Mykytsey
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Abstract

We study g-dimonoids, which are algebraic structures equipped with two associative binary operations satisfying a prescribed system of axioms. We develop a construction of g-dimonoids based on inflations of semigroups, construct several classes of 2-dinilpotent commutative g-dimonoids, and investigate the isomorphism problem for these classes. As an application of these results, we obtain a structural description of all commutative g-dimonoids of order 3, up to isomorphism.

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Cite

BibTeXRIS
BibTeX
@misc{gavrylkiv2026certain,
  title = {{On certain classes of commutative g-dimonoids}},
  author = {Volodymyr Gavrylkiv and Inna Hlushak and Kateryna Koporkh and Natalia Mazurenko and Oksana Mykytsey},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.37933},
  eprint = {2609.37933},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.37933},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On certain classes of commutative g-dimonoids
AU  - Volodymyr Gavrylkiv
AU  - Inna Hlushak
AU  - Kateryna Koporkh
AU  - Natalia Mazurenko
AU  - Oksana Mykytsey
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.37933
UR  - https://arxiv.org/abs/2609.37933
AB  - We study g-dimonoids, which are algebraic structures equipped with two associative binary operations satisfying a prescribed system of axioms. We develop a construction of g-dimonoids based on inflations of semigroups, construct several classes of 2-dinilpotent commutative g-dimonoids, and investigate the isomorphism problem for these classes. As an application of these results, we obtain a structural description of all commutative g-dimonoids of order 3, up to isomorphism.
ER  -