FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2011/2012, VOLUME 17, NUMBER 5, PAGES 129-146

**The atomic theory of left division of two-sided ideals of semirings
with unit**

A. E. Pentus

M. R. Pentus

Abstract

View as HTML
View as gif image

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 $$Í 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.

Location: http://mech.math.msu.su/~fpm/eng/k1112/k115/k11508h.htm

Last modified: October 18, 2012