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

Lomonosov Moscow State University
Moscow Institute of Physics and Technology
University of Manchester

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

12 Scopus citations

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

Bibliographical note

Publisher Copyright:
© 2018

Funding

The research contained in this article was started in 2012 during a visit of the first author to the University of Manchester, funded by EPSRC grant EP/I005293/1 (Nonlinear Eigenvalue Problems: Theory and Numerics). He is grateful to the School of Mathematics and the Tropical Mathematics Group for their warm hospitality. He also thanks RFBR grant 17-01-00895 for partial financial support of his research. The authors thank the referee for his/her valuable suggestions, and in particular, for suggesting the proof of Lemma 4.2 .

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/I005293/1
Russian Foundation for Basic Research	17-01-00895

Keywords

Boolean semiring
Green's relations
Linear preservers
Semifield
Tropical semiring

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ER -

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

Abstract

Bibliographical note

Funding

Keywords

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