SOME CONSEQUENCES OF A FATOU PROPERTY OF THE TROPICAL SEMIRING

Authors
Citation
D. Krob, SOME CONSEQUENCES OF A FATOU PROPERTY OF THE TROPICAL SEMIRING, Journal of pure and applied algebra, 93(3), 1994, pp. 231-249
Citations number
9
Categorie Soggetti
Mathematics, Pure",Mathematics,Mathematics,Mathematics
ISSN journal
00224049
Volume
93
Issue
3
Year of publication
1994
Pages
231 - 249
Database
ISI
SICI code
0022-4049(1994)93:3<231:SCOAFP>2.0.ZU;2-I
Abstract
We show that the equatorial semiring Z(min) = (Z or { + infinity}, min , + ) is a Fatou extension of the tropical semiring M = (N or { + infi nity}, min, + ). This property allows us to give partial decidability results for the equality problem for rational series with multipliciti es in the tropical semiring. We also deduce from it the decidability o f the limitedness problem for the equatorial semiring, solving therefo re a question of 1. Simon.