Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1803-80
Keywords
Tropical algebra, basis submatrix, nonsingular idempotent matrix, regular matrix
First Page
2061
Last Page
2070
Recommended Citation
YANG, LIN
(2018)
"Regular $\mathscr{D}$-classes of the semigroup of $n\times n$ tropical matrices,"
Turkish Journal of Mathematics: Vol. 42:
No.
4, Article 40.
https://doi.org/10.3906/mat-1803-80
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss4/40
