- Turkish Journal of Mathematics
- Vol: 42 Issue: 4
- Regular $\mathscr{D}$-classes of the semigroup of $n\times n$ tropical matrices
Regular $\mathscr{D}$-classes of the semigroup of $n\times n$ tropical matrices
Authors : Lin Yang
Pages : 2061-2070
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :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.Keywords : Tropical algebra, basis submatrix, nonsingular idempotent matrix, regular matrix