Abstract
We show that any semigroup of n-by-n tropical matrices whose elements all have rank n (i.e., a nonsingular semigroup) satisfies a class of nontrivial semigroup identities. These identities generalize the identities satisfied by the monoid of all n-by-n triangular tropical matrices.
| Original language | English |
|---|---|
| Pages (from-to) | 712-732 |
| Number of pages | 21 |
| Journal | Semigroup Forum |
| Volume | 92 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1 Jun 2016 |
| Externally published | Yes |
Keywords
- Nonsingular matrices
- Rank-maximal semigroups
- Semigroup identities
- Semigroup representations
- Semigroup varieties
- Tropical (max-plus) matrix algebra