Email this article The Atomic Theory of Division and Intersection of Semiring Ideals
- Authors: Pentus A.E.1, Pentus M.R.1,2,3,4
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Affiliations:
- Moscow State University
- Russian State University for the Humanities
- Moscow State Pedagogical University
- Steklov Mathematical Institute, Russian Academy of Sciences
- Issue: Vol 233, No 5 (2018)
- Pages: 724-731
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241658
- DOI: https://doi.org/10.1007/s10958-018-3960-4
- ID: 241658
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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 ⊆ 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.
About the authors
A. E. Pentus
Moscow State University
Author for correspondence.
Email: apentus@mech.math.msu.su
Russian Federation, Moscow
M. R. Pentus
Moscow State University; Russian State University for the Humanities; Moscow State Pedagogical University; Steklov Mathematical Institute, Russian Academy of Sciences
Email: apentus@mech.math.msu.su
Russian Federation, Moscow; Moscow; Moscow; Moscow
