Geodesic
The atomic theory of division of semiring ideals
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 201-208.

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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 two function symbols that denote the right 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. 
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A. E. Pentus; M. R. Pentus. The atomic theory of division of semiring ideals. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 2, pp. 201-208. http://geodesic.mathdoc.fr/item/FPM_2006_12_2_a13/

[1] Lambek I., “Matematicheskoe issledovanie struktury predlozheniya”, Matematicheskaya lingvistika: Sbornik perevodov, ed. Yu. A. Shreidera i dr., Mir, M., 1964, 47–68

[2] Fuks L., Chastichno uporyadochennye algebraicheskie sistemy, Mir, M., 1965 | MR

[3] Buszkowski W., “Compatibility of categorial grammar with an associated category system”, Z. Math. Logik Grundlag. Math., 28 (1982), 229–238 | DOI | MR | Zbl

[4] Buszkowski W., “Type logics in grammar”, Trends in Logic: 50 Years of Studia Logica, eds. V. F. Hendricks, J. Malinowski, Kluwer Academic, 2003, 337–382 | MR | Zbl

[5] Van Benthem J., Studies in Logic and the Foundations of Mathematics, 130, North-Holland, Amsterdam, 1991 | MR | Zbl