Generating the monoid of $2 \times 2$ matrices over max-plus and min-plus semirings

James East; Julius Jonušas; J. D. Mitchell

Generating the monoid of $2 \times 2$ matrices over max-plus and min-plus semirings

Rings and Algebras 2020-09-23 v1

Authors: James East , Julius Jonušas , J. D. Mitchell

Abstract

In this short note, we describe generating sets for the monoids of consisting of all $2 \times 2$ matrices over certain finite tropical semirings.

Keywords

monoids matrix semirings max-plus semiring min-plus semiring tropical semirings generating sets

Cite

@article{arxiv.2009.10372,
  title  = {Generating the monoid of $2 \times 2$ matrices over max-plus and min-plus semirings},
  author = {James East and Julius Jonušas and J. D. Mitchell},
  journal= {arXiv preprint arXiv:2009.10372},
  year   = {2020}
}