Abstract: The notion of Γ-semirings was introduced by Murali Krishna Rao as a generalization of the notion of Γ-rings as well as of semirings. We have known that the notion of Γ-semirings is a generalization of the notion of semirings. In this paper, extending Kaushik, Moin and Khan’s work, we generalize the notion of generalized bi-Γ-ideals of Γ-semirings and investigate some related properties of generalized bi-Γ-ideals.
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.