The finite basis problem for the monoid of 2 by 2 upper triangular tropical matrices

Abstract

For each positive $n$, let $u_n=v_n$ denote the identity obtained from the Adjan identity $(xy)(yx)(xy)(xy)(yx)=(xy)(yx)(yx)(xy)(yx)$ by substituting $(xy)\to (x_1{x}_2\dots x_n)$ and $(yx)\to (x_n\dots x_2{x}_1)$. We show that every monoid which satisfies $u_n=v_n$ for each positive $n$ and generates the variety containing the bicyclic monoid is nonfinitely based. This implies that the monoid of 2 by 2 upper triangular tropical matrices over the tropical semiring is nonfinitely based.

published in Bull. Aust. Math. Soc

Cited by in corpus (1)

• Identities in Upper Triangular Tropical Matrix Semigroups and the Bicyclic Monoid