*-QUASIIDEALS IN INVOLUTION SEMIGROUPS

Usama A. Aburawash, Allam A. Allam

Abstract


Let S be an involution semigroup. Then every *-minimal *-quasiideal
of S is a minimal *-quasiideal of S. Nevertheless, if S possesses a primitive idempotent ethen 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.


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