Regular $\\mathscr{D}$-classes of the semigroup of $n\\times n$ tropical matrices
Lin Yang · DergiPark (Istanbul University) · 2018
In this paper we give the characterizations of Green's relations $\\mathscr{R}$, $\\mathscr{L}$, and $\\mathscr{D}$ on the set of matrices with entries in a tropical semiring. An $m\\times n$ tropical matrix $A$ is called regular if there exists an $n\\times m$ tropical matrix $X$ satisfying $AXA = A$. Furthermore, we study the regular $\\mathscr{D}$-classes of the semigroup of all $n\\times n$ tropical matrices under multiplication and give a partition of a nonsingular regular $\\mathscr{D}$-class.