LINEAR ISOMORPHISMS PRESERVING GREEN'S RELATIONS FOR MATRICES OVER ANTI-NEGATIVE SEMIFIELDS

Alexander  Guterman; Marianne Johnson; Mark Kambites

doi:10.1016/j.laa.2018.01.023

LINEAR ISOMORPHISMS PRESERVING GREEN'S RELATIONS FOR MATRICES OVER ANTI-NEGATIVE SEMIFIELDS

Alexander Guterman, Marianne Johnson, Mark Kambites

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Abstract

In this paper we characterize those linear bijective maps on the monoid of all n×n square matrices over an anti-negative semifield (that is, a semifield which is not a field) which preserve each of Green's equivalence relations L, R, H, D, J and the corresponding four pre-orderings ≤L, ≤R, ≤H, ≤J. These results apply in particular to the tropical and boolean semirings.

Original language	English
Journal	Linear Algebra and its Applications
Early online date	3 Feb 2018
DOIs	https://doi.org/10.1016/j.laa.2018.01.023
Publication status	Published - 2018

Keywords

Green's relations
linear preservers
semield
tropical semiring,
boolean semiring

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10.1016/j.laa.2018.01.023

GutermanJohnsonKambites_revised_finalAccepted author manuscript, 315 KBLicence: CC BY-NC-ND

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title = "LINEAR ISOMORPHISMS PRESERVING GREEN'S RELATIONS FOR MATRICES OVER ANTI-NEGATIVE SEMIFIELDS",

abstract = "In this paper we characterize those linear bijective maps on the monoid of all n×n square matrices over an anti-negative semifield (that is, a semifield which is not a field) which preserve each of Green's equivalence relations L, R, H, D, J and the corresponding four pre-orderings ≤L, ≤R, ≤H, ≤J. These results apply in particular to the tropical and boolean semirings.",

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author = "Alexander Guterman and Marianne Johnson and Mark Kambites",

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language = "English",

journal = "Linear Algebra and its Applications",

issn = "0024-3795",

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AU - Guterman, Alexander

AU - Johnson, Marianne

AU - Kambites, Mark

PY - 2018

Y1 - 2018

N2 - In this paper we characterize those linear bijective maps on the monoid of all n×n square matrices over an anti-negative semifield (that is, a semifield which is not a field) which preserve each of Green's equivalence relations L, R, H, D, J and the corresponding four pre-orderings ≤L, ≤R, ≤H, ≤J. These results apply in particular to the tropical and boolean semirings.

AB - In this paper we characterize those linear bijective maps on the monoid of all n×n square matrices over an anti-negative semifield (that is, a semifield which is not a field) which preserve each of Green's equivalence relations L, R, H, D, J and the corresponding four pre-orderings ≤L, ≤R, ≤H, ≤J. These results apply in particular to the tropical and boolean semirings.

KW - Green's relations

KW - linear preservers

KW - semield

KW - tropical semiring,

KW - boolean semiring

U2 - 10.1016/j.laa.2018.01.023

DO - 10.1016/j.laa.2018.01.023

M3 - Article

SN - 0024-3795

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

LINEAR ISOMORPHISMS PRESERVING GREEN'S RELATIONS FOR MATRICES OVER ANTI-NEGATIVE SEMIFIELDS

Abstract

Keywords

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