Finite Semimodules Over Three-element Multiplicatively Idempotent Semirings
- Autores: Vechtomov E.M.1, Petrov A.A.1, Shklyaev A.P.1
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Afiliações:
- Vyatka State University
- Edição: Nº 3 (66) (2024)
- Páginas: 5-15
- Seção: Mathematics
- URL: https://ogarev-online.ru/1993-0550/article/view/307278
- DOI: https://doi.org/10.17072/1993-0550-2024-3-5-15
- ID: 307278
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Resumo
In this paper we study the structure of finite semimodules over three-element multiplicatively idempotent semirings. The main attention is paid to the case of three-element idempotent semirings. Semimodules containing at most 6 elements over three-element idempotent semirings are described.
Sobre autores
E. Vechtomov
Vyatka State University
Autor responsável pela correspondência
Email: vecht@mail.ru
Doctor of Physical and Mathematical Sciences, Professor, Head of the Department of Fundamental Mathematics 36, Moskovskaya St., Kirov, Russia, 610000
A. Petrov
Vyatka State University
Email: apetrov43@mail.ru
Candidate of Physical and Mathematical Sciences, Associate Professor of Department of Fundamental Mathematics 36, Moskovskaya St., Kirov, Russia, 610000
A. Shklyaev
Vyatka State University
Email: sascha.schlyaev@yandex.ru
Bachelor of the Fourth Year of Study in the Field of Mathematics and Computer Science 36, Moskovskaya St., Kirov, Russia, 610000
Bibliografia
- Vechtomov, E. M. (2024), "On semimodules over multiplica-tively idempotent semirings", International Scientific Conference "Algebra and Mathematical Logic: theory and applications", KFU, Kazan, pp. 103–104.
- Petrov, A. A. (2024), "On commutative additive semigroups with identity 4x=2x", International Scientific Conference "Al-gebra and Mathematical Logic: Theory and Applications", KFU, Kazan, pp. 130–131.
- Vechtomov, E. M. and Petrov, A. A. (2022), "Functional alge-bra and semirings. Semirings with idempotent multiplication", Lan, St. Petersburg, 180 p.
- Fofanova, T. S. (1982), "Polygons over distributive lattices", Universal Algebra / Colloq. Math. Soc. J. Bolyai, North-Holland, Amsterdam, pp. 289–292.
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- Kozhukhov, I. B. and Mikhalev, A. V. (2020), "Polygons over semigroups", Fundamental and applied mathematics, Vol. 23, Iss. 3, pp. 141–199.
- Il’in, S. N. (2018), "On the homological classification of semir-ings", Results of science and technology. Series. Modern math-ematics and its applications. Thematic reviews, Vol. 158, pp. 3–22.
- Golan, J. S. (1999), "Semirings and their applications", Kluwer Academic Publishers, Dordrecht, 382 p.
- Grätzer, G. (1982), "General lattice theory", Mir, M., 456 p.
- Fofanova, T. S. (1971), "Polygons over distributive structures", Siberian Mathematical Journal, Vol. 12, no. 5, pp. 1158–1163.
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