Abstract
We show that the monoid of 2×2 tropical matrices is a regular semigroup satisfying the semigroup identity Studying reduced identities for subsemigroups of and introducing a faithful semigroup representation for the bicyclic monoid by 2×2 tropical matrices, we reprove Adjan's identity for the bicyclic monoid in a much simpler way.
Original language | English |
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Pages (from-to) | 191-218 |
Number of pages | 28 |
Journal | Semigroup Forum |
Volume | 80 |
Issue number | 2 |
DOIs | |
State | Published - 2010 |
Externally published | Yes |
Keywords
- Idempotent semiring
- Monoid representation
- Regular monoids
- Semigroup identity
- Tropical (max-plus) matrix algebra