The solvable conditions of linear system over commutative semirings

  • Qian-yu Shu
  • Xue-ping WangEmail author


This paper deals with the solution of linear system over commutative semirings. It uses the bideterminant of a matrix to investigate the solvable conditions of a system of linear equations and gives some necessary and sufficient conditions that a system of linear equations is solvable.


Bideterminant Linear system The solvable condition 



The authors thank the referees for their valuable comments and suggestions. Supported by National Natural Science Foundation of China (No. 61573240), Postdoctoral Science Foundation of Jiangsu Province (No. 2018K031A) and Postdoctoral Science Foundation of China (No. 2018M642203).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animal participants

This article does not contain any studies with human participants or animals performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and Software ScienceSichuan Normal UniversityChengduPeople’s Republic of China

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