Semigroup identities in the monoid of triangular tropical matrices

Zur Izhakian

doi:https://doi.org/10.1007/s00233-013-9507-6

Semigroup identities in the monoid of triangular tropical matrices

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

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
DOIs	https://doi.org/10.1007/s00233-013-9507-6
State	Published - Feb 2014
Externally published	Yes

Keywords

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

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1007/s00233-013-9507-6

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.",

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

author = "Zur Izhakian",

year = "2014",

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doi = "https://doi.org/10.1007/s00233-013-9507-6",

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T1 - Semigroup identities in the monoid of triangular tropical matrices

AU - Izhakian, Zur

PY - 2014/2

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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 - Idempotent semirings

KW - Monoid representations

KW - Semigroup identities

KW - Semigroup varieties

KW - Tropical (max-plus) matrix algebra

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U2 - https://doi.org/10.1007/s00233-013-9507-6

DO - https://doi.org/10.1007/s00233-013-9507-6

M3 - مقالة

SN - 0037-1912

VL - 88

SP - 145

EP - 161

JO - Semigroup Forum

JF - Semigroup Forum

IS - 1

ER -

Semigroup identities in the monoid of triangular tropical matrices

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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