@article{8b1f4c459f0d4cb29c48afb00ce7188d,
title = "Semigroup identities in the monoid of two-by-two tropical matrices",
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.",
keywords = "Idempotent semiring, Monoid representation, Regular monoids, Semigroup identity, Tropical (max-plus) matrix algebra",
author = "Zur Izhakian and Margolis, {Stuart W.}",
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. ",
year = "2010",
doi = "10.1007/s00233-009-9203-8",
language = "אנגלית",
volume = "80",
pages = "191--218",
journal = "Semigroup Forum",
issn = "0037-1912",
publisher = "Springer New York",
number = "2",
}