*-QUASIIDEALS IN INVOLUTION SEMIGROUPS

Abstract

Let S be an involution semigroup. Then every *-minimal *-quasiideal

of S is a minimal *-quasiideal of S. Nevertheless, if S possesses a prim

itive idempotent e then the *-quasiideal eSe∗ (e∗Se) is minimal if and

only if it is a (von Neumann) regular *-subsemigroup. Furthermore, S is

*-simple if and only if it is simple. Finally, if S has a minimal *-quasiideal

then it has a completely simple kernel K and the minimal *-quasiideals

of S are just the *-maximal *-subgroups of K.