Semigroup identities of supertropical matrices

Zur Izhakian; Glenn Merlet

doi:10.1007/s00233-022-10283-5

Semigroup identities of supertropical matrices

Zur Izhakian, Glenn Merlet

Department of Mathematics

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

Abstract

We prove that, for any n, the monoid of all n× n supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities; in particular, such supertropical triangular matrices admit exactly the same identities satisfied by tropical triangular matrices. These semigroup identities are carried over to labeled-weighted digraphs with double arcs.

Original language	English
Pages (from-to)	466-477
Number of pages	12
Journal	Semigroup Forum
Volume	105
Issue number	2
DOIs	https://doi.org/10.1007/s00233-022-10283-5
State	Published - Oct 2022

Keywords

Idempotent semirings
Semigroup identities
Semigroup representations
Supertropical matrices
Tropical (max-plus) matrices
Weighted diagraphs

Access to Document

10.1007/s00233-022-10283-5

Cite this

@article{641520376a9a4a5981e1b720ec7683ff,

title = "Semigroup identities of supertropical matrices",

abstract = "We prove that, for any n, the monoid of all n× n supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities; in particular, such supertropical triangular matrices admit exactly the same identities satisfied by tropical triangular matrices. These semigroup identities are carried over to labeled-weighted digraphs with double arcs.",

keywords = "Idempotent semirings, Semigroup identities, Semigroup representations, Supertropical matrices, Tropical (max-plus) matrices, Weighted diagraphs",

author = "Zur Izhakian and Glenn Merlet",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2022",

month = oct,

doi = "10.1007/s00233-022-10283-5",

language = "אנגלית",

volume = "105",

pages = "466--477",

journal = "Semigroup Forum",

issn = "0037-1912",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Semigroup identities of supertropical matrices

AU - Izhakian, Zur

AU - Merlet, Glenn

PY - 2022/10

Y1 - 2022/10

N2 - We prove that, for any n, the monoid of all n× n supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities; in particular, such supertropical triangular matrices admit exactly the same identities satisfied by tropical triangular matrices. These semigroup identities are carried over to labeled-weighted digraphs with double arcs.

AB - We prove that, for any n, the monoid of all n× n supertropical matrices extending tropical matrices satisfies nontrivial semigroup identities; in particular, such supertropical triangular matrices admit exactly the same identities satisfied by tropical triangular matrices. These semigroup identities are carried over to labeled-weighted digraphs with double arcs.

KW - Idempotent semirings

KW - Semigroup identities

KW - Semigroup representations

KW - Supertropical matrices

KW - Tropical (max-plus) matrices

KW - Weighted diagraphs

UR - http://www.scopus.com/inward/record.url?scp=85136160476&partnerID=8YFLogxK

U2 - 10.1007/s00233-022-10283-5

DO - 10.1007/s00233-022-10283-5

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

AN - SCOPUS:85136160476

SN - 0037-1912

VL - 105

SP - 466

EP - 477

JO - Semigroup Forum

JF - Semigroup Forum

IS - 2

ER -

Semigroup identities of supertropical matrices

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this