FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 2, PAGES 169-189

**The atomic theory of multiplication and 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 three function
symbols that denote the multiplication, right division, 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.

Location: http://mech.math.msu.su/~fpm/eng/k09/k092/k09208h.htm

Last modified: December 22, 2009