Type-II conjecture is true for finite I-trivial monoids

Karsten Henckell, John Rhodes
1992 Journal of Algebra  
We discuss the importance of determining M" for any finite monoid h4. We prove that if all regular elements of the finite monoid M are type-II eIements (a decidable condition which includes d-triviat), then the strong type-11 conjecture is true for M, I.e., M,=M,F, and so M,{ is decidable. As an application we prove that for P(G), the monoid of nonempty subsets of a finite group G, [P(G)]"= [P(G)],r holds.
doi:10.1016/0021-8693(92)90141-8 fatcat:xr22vzrpnnhqfonfcljt22dnwe