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 |
|---|---|
| Pages (from-to) | 191-218 |
| Number of pages | 28 |
| Journal | Semigroup Forum |
| Volume | 80 |
| Issue number | 2 |
| DOIs | |
| State | Published - 2010 |
Bibliographical note
Funding Information:The first author has been supported by the Chateaubriand scientific post-doctorate fellowships, Ministry of Science, French Government, 2007–2008; and was partially supported by a grant from the European Science Foundation (ESF), Automata: from Mathematics to Applications, No. 1609, 2007.
Funding
The first author has been supported by the Chateaubriand scientific post-doctorate fellowships, Ministry of Science, French Government, 2007–2008; and was partially supported by a grant from the European Science Foundation (ESF), Automata: from Mathematics to Applications, No. 1609, 2007.
| Funders | Funder number |
|---|---|
| Ministry of Science, French Government | |
| European Science Foundation | 1609 |
Keywords
- Idempotent semiring
- Monoid representation
- Regular monoids
- Semigroup identity
- Tropical (max-plus) matrix algebra