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Fundamentalnaya i Prikladnaya Matematika, 2009, Volume 15, Issue 2, Pages 169–189 (Mi fpm1219)  
The atomic theory of multiplication and division of semiring ideals

A. E. Pentus, M. R. Pentus

M. V. Lomonosov Moscow State 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 multiplication, right division, and left division of ideals. We prove that the set of those atomic formulas in this signature that are valid for all semirings and all valuations is decidable.
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 167, Issue 6, Pages 841–856
DOI: https://doi.org/10.1007/s10958-010-9964-3
Bibliographic databases:
UDC: 512+510.64
Language: Russian
Citation: A. E. Pentus, M. R. Pentus, “The atomic theory of multiplication and division of semiring ideals”, Fundam. Prikl. Mat., 15:2 (2009), 169–189; J. Math. Sci., 167:6 (2010), 841–856
Citation in format AMSBIB
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\by A.~E.~Pentus, M.~R.~Pentus
\paper The atomic theory of multiplication and division of semiring ideals
\jour Fundam. Prikl. Mat.
\yr 2009
\vol 15
\issue 2
\pages 169--189
\mathnet{http://mi.mathnet.ru/fpm1219}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2744963}
\transl
\jour J. Math. Sci.
\yr 2010
\vol 167
\issue 6
\pages 841--856
\crossref{https://doi.org/10.1007/s10958-010-9964-3}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954033027}
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    		Фундаментальная и прикладная математика
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