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

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

14 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

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

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

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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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T1 - Semigroup identities in the monoid of triangular tropical matrices

AU - Izhakian, Zur

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.

PY - 2014/2

Y1 - 2014/2

N2 - 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.

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

M3 - Article

VL - 88

SP - 145

EP - 161

JO - Semigroup Forum

JF - Semigroup Forum

SN - 0037-1912

IS - 1

ER -

Semigroup identities in the monoid of triangular tropical matrices

Abstract

Keywords

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