On semiprime, Prime and Strongly Prime-bi-ideals in Semigroup with Involution

In [1] Ahsan and Liu has characterized the prime (semiprime) ideals and right ideals for a semigroup. Furthermore G. Szasz[5] has considered semigroups in which ideals are prime. He has also shown that the ideals of a semigroup P are prime if and only if P is intra regular. In this paper we have introduce the concept of semiprime, prime and strongly prime-bi-ideals in semigroups with involution. Also we have given characterizations for involution semigroups whose bi-ideals are having all the above properties. Furthermore we have investigated their structural properties by attaching involution on their corresponding ground semigroups. For every involution semigroup S we denote -bi-ideal for bi-ideals in involution semigroup.