Permutability of matrices over bipotent semirings

Thomas Aird, Mark Kambites

Research output: Contribution to journalArticlepeer-review


We study permutability properties of matrix semigroups over commutative bipotent semirings (of which the best-known example is the tropical semiring). We prove that every such semigroup is weakly permutable (a result previous stated in the literature, but with an erroneous proof) and then proceed to study in depth the question of when they are strongly permutable (which turns out to depend heavily on the semiring). Along the way we classify monogenic bipotent semirings and
describe all isomorphisms between truncated tropical semirings.
Original languageEnglish
JournalSemigroup Forum
Early online date24 Mar 2022
Publication statusPublished - 24 Mar 2022


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