Abstract: Using the idea of prime and semiprime bi-ideals of
rings, the concept of prime and semiprime generalized bi-ideals of
rings is introduced, which is an extension of the concept of prime and
semiprime bi-ideals of rings and some interesting characterizations
of prime and semiprime generalized bi-ideals are obtained. Also,
we give the relationship between the Baer radical and prime and
semiprime generalized bi-ideals of rings in the same way as of biideals
of rings which was studied by Roux.