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Ural Mathematical Journal, 2020, Volume 6, Issue 2, Pages 117–132
DOI: https://doi.org/10.15826/umj.2020.2.012 (Mi umj132) 		 
This article is cited in 5 scientific papers (total in 5 papers)

The variety generated by an ai-semiring of order three

Xianzhong Zhaoa, Miaomiao Rena, Siniša Crvenkovićb, Yong Shaoa, Petar Dapićb

a Northwest University
b University of Novi Sad
Full-text PDF (206 kB) Citations (5)
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DOI: https://doi.org/10.15826/umj.2020.2.012
Abstract: Up to isomorphism, there are 61 ai-semirings of order three. The finite basis problem for these semirings is investigated. This problem for 45 semirings of them is answered by some results in the literature. The remaining semirings are studied using equational logic. It is shown that with the possible exception of the semiring $S_7$, all ai-semirings of order three are finitely based.
Keywords: ai-semiring, identity, finitely based variety.
Funding agency Grant number
National Basic Research Program of China 11971383
11571278
11701449
Shaanxi Province Natural Science Foundation of China 2020JM-425
Xianzhong Zhao is supported by National Natural Science Foundation of China (11971383, 11571278). Miaomiao Ren, corresponding author, is supported by National Natural Science Foundation of China (11701449). Yong Shao is supported by Natural Science Foundation of Shaanxi Province (2020JM-425).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Xianzhong Zhao, Miaomiao Ren, Siniša Crvenković, Yong Shao, Petar Dapić, “The variety generated by an ai-semiring of order three”, Ural Math. J., 6:2 (2020), 117–132
Citation in format AMSBIB
\Bibitem{ZhaRenCrv20}
\by Xianzhong~Zhao, Miaomiao~Ren, Sini{\v s}a~Crvenkovi\'c, Yong~Shao, Petar~Dapi\'c
\paper The variety generated by an ai-semiring of order three
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 2
\pages 117--132
\mathnet{http://mi.mathnet.ru/umj132}
\crossref{https://doi.org/10.15826/umj.2020.2.012}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4194020}
\elib{https://elibrary.ru/item.asp?id=44611156}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85099533675}
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    • This publication is cited in the following 5 articles:
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