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

Research output: Contribution to journal › Article

8 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

Keywords

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

Access to Document

10.1007/s00233-013-9507-6Licence: Unspecified

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

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Izhakian, Z. (2014). Semigroup identities in the monoid of triangular tropical matrices. Semigroup Forum, 88(1), 145-161. https://doi.org/10.1007/s00233-013-9507-6

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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.",

keywords = "Tropical (max-plus) matrix algebra, Idempotent semirings, Semigroup identities, Semigroup varieties, Monoid representations",

author = "Zur Izhakian",

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.",

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N1 - 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.

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AB - 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.

KW - Tropical (max-plus) matrix algebra

KW - Idempotent semirings

KW - Semigroup identities

KW - Semigroup varieties

KW - Monoid representations

U2 - 10.1007/s00233-013-9507-6

DO - 10.1007/s00233-013-9507-6

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JO - Semigroup Forum

JF - Semigroup Forum

SN - 0037-1912

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