A countable family of finitely presented infinite congruence-free monoids

Alan J. Cain, Victor Maltcev, Abdullahi Umar

We prove that monoids $\mathrm{Mon}⟨a,b,c,d:a^{n}b=0,ac=1,db=1,dc=1,dab=1,d{a}^{2}b=1,\dots ,d{a}^{n-1}b=1⟩$ are congruence-free for all $n\ge 1$. This provides a ne…