The Baer Radical of Rings in Term of Prime and Semiprime Generalized Bi-ideals

Authors: Rattiya Boonruang, Aiyared Iampan

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.

Keywords: ring, prime and semiprime (generalized) bi-ideal, Baer radical.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085038

References:

[1] K. R. Goodearl and R. B. Warfield Jr, An Introduction to Noncommutative Noetherian Rings, Cambridge University, 2004.
[2] T. W. Hungerford, Algebra, Department of Mathematics, Cleveland State University, USA, 1974.
[3] S. Lajos and F. A. Sz'asz, Bi-ideals in associative rings, Acta Sci. Math. 32, 185-193, 1971.
[4] H. J. L. Roux, A note on prime and semiprime bi-ideals, Kyungpook Math. J. 35, 243-247, 1995.
[5] F. A. Sz'asz, Generalized biideals of rings. I, Mathematische Nachrichten 47, 355-360, 1970.
[6] F. A. Sz'asz, Generalized biideals of rings. II, Mathematische Nachrichten 47, 361-364, 1970.
[7] A. P. J. van der Walt, Prime and semiprime bi-ideals, Quaestiones Mathematicae 5, 341-345, 1983.