Commenced in January 2007
Paper Count: 31108
The Baer Radical of Rings in Term of Prime and Semiprime Generalized Bi-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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085038Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1012
 K. R. Goodearl and R. B. Warfield Jr, An Introduction to Noncommutative Noetherian Rings, Cambridge University, 2004.
 T. W. Hungerford, Algebra, Department of Mathematics, Cleveland State University, USA, 1974.
 S. Lajos and F. A. Sz'asz, Bi-ideals in associative rings, Acta Sci. Math. 32, 185-193, 1971.
 H. J. L. Roux, A note on prime and semiprime bi-ideals, Kyungpook Math. J. 35, 243-247, 1995.
 F. A. Sz'asz, Generalized biideals of rings. I, Mathematische Nachrichten 47, 355-360, 1970.
 F. A. Sz'asz, Generalized biideals of rings. II, Mathematische Nachrichten 47, 361-364, 1970.
 A. P. J. van der Walt, Prime and semiprime bi-ideals, Quaestiones Mathematicae 5, 341-345, 1983.