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 Fundam. Prikl. Mat., 2012, Volume 17, Issue 5, Pages 129–146 (Mi fpm1438)

The atomic theory of left division of two-sided ideals of semirings with unit

A. E. Pentus, M. R. Pentus

M. V. Lomonosov Moscow State University

Abstract: We consider two-sided ideals of semirings with unit. We study the theory of two-sided ideals in the signature consisting of the binary predicate symbol $\subseteq$ and a binary function symbol that denotes the left division of ideals. We prove the polynomial-time decidability of the problem of deciding whether a given atomic formula in this signature is valid for all semirings with unit and all valuations. A similar result holds for atomic formulas with the right division, but without the left division.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:4, 566–579

UDC: 512+510.64

Citation: A. E. Pentus, M. R. Pentus, “The atomic theory of left division of two-sided ideals of semirings with unit”, Fundam. Prikl. Mat., 17:5 (2012), 129–146; J. Math. Sci., 193:4 (2013), 566–579

Citation in format AMSBIB
\Bibitem{PenPen12} \by A.~E.~Pentus, M.~R.~Pentus \paper The atomic theory of left division of two-sided ideals of semirings with unit \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 5 \pages 129--146 \mathnet{http://mi.mathnet.ru/fpm1438} \transl \jour J. Math. Sci. \yr 2013 \vol 193 \issue 4 \pages 566--579 \crossref{https://doi.org/10.1007/s10958-013-1483-6} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899407652}