FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 2, PAGES 201-208

The atomic theory of division of semiring ideals

A. E. Pentus
M. R. Pentus

Abstract

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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 $$Í 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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Last modified: June 17, 2006