Lin YANG

14687

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

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,

Turkish Journal of Mathematics-Cover

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

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