Regular D -classes of the semigroup of n × n tropical matrices

Abstract

In this paper we give the characterizations of Green’s relations R , L , and D on the set of matrices withentries in a tropical semiring. An m × n tropical matrix A is called regular if there exists an n × m tropical matrixX satisfying AXA = A. Furthermore, we study the regular D -classes of the semigroup of all n × n tropical matricesunder multiplication and give a partition of a nonsingular regular D -class.