Abstract. It is shown that the semigroup variety generated by the monoid $$ A_{0}^1 = \langle a, b : a^2 = a, b^2 = b, ba = 0 \rangle\cup \{1 \} $$ of order five is hereditarily finitely based and contains countably infinitely many subvarieties. In contrast, the monoid variety generated by $A_{0}^1$ is shown to contain only eight subvarieties.

AMS Subject Classification (1991): 20M07, 08B15, 03C05

Keyword(s): semigroups, monoids, varieties, finitely based, hereditarily finitely based

Received July 4, 2007, and in revised form October 31, 2007. (Registered under 6030/2009.)