Semigroup identities in the monoid of triangular tropical matrices

Zur Izhakian

doi:10.1007/s00233-013-9507-6

Semigroup identities in the monoid of triangular tropical matrices

Zur Izhakian

Mathematical Science

University of Bremen

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

17 Citations (Scopus)

Abstract

We show that the submonoid of all n×n triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities.

Original language	English
Pages (from-to)	145-161
Number of pages	17
Journal	Semigroup Forum
Volume	88
Issue number	1
Early online date	22 Jun 2013
DOIs	https://doi.org/10.1007/s00233-013-9507-6
Publication status	Published - Feb 2014

Bibliographical note

The author thanks Glenn Merlet for the useful conversation in CIRM, Luminy, September 2011. The author would like to thank the referee for many valuable comments and helpful suggestions.

Keywords

Tropical (max-plus) matrix algebra
Idempotent semirings
Semigroup identities
Semigroup varieties
Monoid representations

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https://arxiv.org/abs/1305.3903Licence: Unspecified

Cite this

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title = "Semigroup identities in the monoid of triangular tropical matrices",

abstract = "We show that the submonoid of all n×n triangular tropical matrices satisfies a nontrivial semigroup identity and provide a generic construction for classes of such identities. The utilization of the Fibonacci number formula gives us an upper bound on the length of these 2-variable semigroup identities.",

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author = "Zur Izhakian",

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KW - Tropical (max-plus) matrix algebra

KW - Idempotent semirings

KW - Semigroup identities

KW - Semigroup varieties

KW - Monoid representations

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SP - 145

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JO - Semigroup Forum

JF - Semigroup Forum

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Semigroup identities in the monoid of triangular tropical matrices

Abstract

Bibliographical note

Keywords

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