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Fundamentalnaya i Prikladnaya Matematika, 2012, Volume 17, Issue 5, Pages 129–146
(Mi fpm1438)
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This article is cited in 3 scientific papers (total in 3 papers)
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.
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
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https://www.mathnet.ru/eng/fpm1438 https://www.mathnet.ru/eng/fpm/v17/i5/p129
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Abstract page: | 331 | Full-text PDF : | 121 | References: | 37 | First page: | 2 |
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