Semigroup identities of tropical matrices through matrix ranks

Autor:	Izhakian, Zur, Merlet, Glenn
Rok vydání:	2018
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics 20M05 20M07 20M30 47D03
Druh dokumentu:	Working Paper
Popis:	We prove the conjecture that, for any $n$, the monoid of all $n \times n$ tropical matrices satisfies nontrivial semigroup identities. To this end, we prove that the factor rank of a large enough power of a tropical matrix does not exceed the tropical rank of the original matrix. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1806.11028 Zobrazit plný text záznamu View this record from Arxiv