Semigroup identities in the monoid of two-by-two tropical matrices

Zur Izhakian; Stuart W. Margolis

doi:10.1007/s00233-009-9203-8

Semigroup identities in the monoid of two-by-two tropical matrices

Zur Izhakian, Stuart W. Margolis

Research output: Contribution to journal › Article › peer-review

32 Scopus citations

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	https://doi.org/10.1007/s00233-009-9203-8
State	Published - 2010
Externally published	Yes

Keywords

Idempotent semiring
Monoid representation
Regular monoids
Semigroup identity
Tropical (max-plus) matrix algebra

Access to Document

10.1007/s00233-009-9203-8

Cite this

@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",

}

TY - JOUR

T1 - Semigroup identities in the monoid of two-by-two tropical matrices

AU - Izhakian, Zur

AU - Margolis, Stuart W.

N1 - 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.

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Idempotent semiring

KW - Monoid representation

KW - Regular monoids

KW - Semigroup identity

KW - Tropical (max-plus) matrix algebra

UR - https://www.scopus.com/pages/publications/77952093031

U2 - 10.1007/s00233-009-9203-8

DO - 10.1007/s00233-009-9203-8

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:77952093031

SN - 0037-1912

VL - 80

SP - 191

EP - 218

JO - Semigroup Forum

JF - Semigroup Forum

IS - 2

ER -

Semigroup identities in the monoid of two-by-two tropical matrices

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this