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

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

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
Pages (from-to)	1-14
Number of pages	14
Journal	Linear Algebra and Its Applications
Volume	545
DOIs	https://doi.org/10.1016/j.laa.2018.01.023
State	Published - 15 May 2018
Externally published	Yes

Keywords

Boolean semiring
Green's relations
Linear preservers
Semifield
Tropical semiring

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2018.01.023

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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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T1 - Linear isomorphisms preserving Green's relations for matrices over anti-negative semifields

AU - Guterman, Alexander

AU - Johnson, Marianne

AU - Kambites, Mark

PY - 2018/5/15

Y1 - 2018/5/15

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 - Boolean semiring

KW - Green's relations

KW - Linear preservers

KW - Semifield

KW - Tropical semiring

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U2 - 10.1016/j.laa.2018.01.023

DO - 10.1016/j.laa.2018.01.023

M3 - مقالة

SN - 0024-3795

VL - 545

SP - 1

EP - 14

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

All Science Journal Classification (ASJC) codes

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