A Class of Eventually Regular Semigroups Determined by Pseudo-Random Sets
Peter M. Higgins · Journal of the London Mathematical Society · 1993
A class of covers of the free monogenic inverse monoid is introduced in one-to-one correspondence with the irrational numbers greater than one. Each member of the class is an eventually regular semigroup with a generator a, the regular powers of which form a pseudo-random set. This then affords an example of a direct product of two eventually regular semigroups that is not eventually regular, thus answering a question of P. M. Edwards.