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

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10.1007/s00233-022-10283-5

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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",

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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

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Semigroup identities of supertropical matrices

Abstract

Keywords

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