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

מתמטיקה

פרסום מחקרי: פרסום בכתב עת › מאמר › ביקורת עמיתים

תקציר

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.

שפה מקורית	אנגלית
עמודים (מ-עד)	466-477
מספר עמודים	12
כתב עת	Semigroup Forum
כרך	105
מספר גיליון	2
מזהי עצם דיגיטלי (DOIs)	https://doi.org/10.1007/s00233-022-10283-5
סטטוס פרסום	פורסם - אוק׳ 2022

גישה למסמך

10.1007/s00233-022-10283-5

קבצים וקישורים אחרים

Link to publication in Scopus

פורמט ציטוט ביבליוגרפי

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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",

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

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T1 - Semigroup identities of supertropical matrices

AU - Izhakian, Zur

AU - Merlet, Glenn

PY - 2022/10

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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 - https://www.scopus.com/pages/publications/85136160476

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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

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