{"references": ["K. R. Goodearl and R. B. Warfield Jr, An Introduction to Noncommutative\nNoetherian Rings, Cambridge University, 2004.", "T. W. Hungerford, Algebra, Department of Mathematics, Cleveland State\nUniversity, USA, 1974.", "S. Lajos and F. A. Sz'asz, Bi-ideals in associative rings, Acta Sci. Math.\n32, 185-193, 1971.", "H. J. L. Roux, A note on prime and semiprime bi-ideals, Kyungpook\nMath. J. 35, 243-247, 1995.", "F. A. Sz'asz, Generalized biideals of rings. I, Mathematische Nachrichten\n47, 355-360, 1970.", "F. A. Sz'asz, Generalized biideals of rings. II, Mathematische Nachrichten\n47, 361-364, 1970.", "A. P. J. van der Walt, Prime and semiprime bi-ideals, Quaestiones\nMathematicae 5, 341-345, 1983."]}

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.