Computer Finding of Four-element Multiplicatively Idempotent Semirings
DOI:
https://doi.org/10.17072/1993-0550-2022-2-46-52Keywords:
finite semiring, idempotence, multiplicatively idempotent semiring, computer modeling.Abstract
In this paper we describe a computer program for searching for all four-element multiplicatively idempotent semirings. We have established that up to the isomorphism of such semirings exactly 381, they are represented by Cayley tables of additive and multiplicative reducts. We give the necessary definitions, properties and illustrations.References
Вечтомов Е.М., Петров А.А. Полукольца с идемпотентным умножением. Киров: Издво ООО "Радуга-ПРЕСС", 2015. 144 с.
Вечтомов Е. М., Петров А. А. Трехэлементные мультипликативно идемпотентные полукольца // Математический вестник Вятского госу-дарственного университета. 2021. №2 (21). С 13–23.
Chaida I., Länger H., Švrček F. Multiplicatively idempotent semirings // Mathematica Bohemica. 2015. V. 140, № 1. P. 35–42.
Golan J. S. Semirings and their applications. Kluwer Academic Publishers: Dordrecht-Boston-London, 1999. 380 p.
Vechtomov Е. М., Petrov А. А. Multiplicatively Idempotent Semirings // Journal of Mathematical Sciences (New York). 2015. V. 206, Issue 6. P. 634–653.
Zhao X., Ren M., Crvenković S., Shao Y., Dapić P. The variety generated by an ai-semiring of order three // Ural Mathematical Journal. 2020. V. 6, Is-sue 2, P. 117–132.
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Copyright (c) 2022 Андрей Александрович Петров, Роман Андреевич Михеев
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles are published under license Creative Commons Attribution 4.0 International (CC BY 4.0).