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Fundamentalnaya i Prikladnaya Matematika, 2016, Volume 21, Issue 1, Pages 181–191 (Mi fpm1711)  
The atomic theory of division and intersection of semiring ideals

A. E. Pentusa, M. R. Pentusbcad

a Lomonosov Moscow State University
b Russian State University for the Humanities
c Steklov Mathematical Institute of Russian Academy of Sciences
d Moscow State Pedagogical University
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Abstract: We consider two-sided ideals of semirings. More precisely, we study the theory of two-sided ideals in the signature consisting of the predicate symbol $ \subseteq $ and three function symbols that denote the intersection, right division, and left division of ideals. We prove the decidability of the set of those atomic formulas in this signature that are valid for all semirings and all valuations.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00127_а
15-01-09218_а
16-01-00615_а
Ministry of Education and Science of the Russian Federation НШ-1423.2014.1
English version:
Journal of Mathematical Sciences (New York), 2018, Volume 233, Issue 5, Pages 724–731
DOI: https://doi.org/10.1007/s10958-018-3960-4
Bibliographic databases:
Document Type: Article
UDC: 512+510.64
Language: Russian
Citation: A. E. Pentus, M. R. Pentus, “The atomic theory of division and intersection of semiring ideals”, Fundam. Prikl. Mat., 21:1 (2016), 181–191; J. Math. Sci., 233:5 (2018), 724–731
Citation in format AMSBIB
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\by A.~E.~Pentus, M.~R.~Pentus
\paper The atomic theory of division and intersection of semiring ideals
\jour Fundam. Prikl. Mat.
\yr 2016
\vol 21
\issue 1
\pages 181--191
\mathnet{http://mi.mathnet.ru/fpm1711}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3660628}
\transl
\jour J. Math. Sci.
\yr 2018
\vol 233
\issue 5
\pages 724--731
\crossref{https://doi.org/10.1007/s10958-018-3960-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85050950733}
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    		Фундаментальная и прикладная математика
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