Abstract. Starting in 2001, Kemprasit and her students showed that certain semigroups of (linear) transformations defined on a set (or on a vector space) belong to $BQ$: that is, the class of semigroups $S$ in which every bi-ideal of $S$ is a quasi-ideal of $S$. Here, we unify that work and show that some of it can be derived from a result for abstract semigroups. We also extend their work, and that of Mendes-Gonçalves and Sullivan, to other examples of transformation semigroup.

AMS Subject Classification (1991): 20M20; 15A04

Keyword(s): quasi-ideal, bi-ideal, BQ, -semigroup, transformation semigroup

Received February 14, 2008, and in revised form October 17, 2008. (Registered under 6061/2009.)