On Continuous Rings

✍ Scribed by Mohamed F. Yousif

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 212 KB
• Volume: 191
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.6936

✦ Synopsis

We show that if R is a semiperfect ring with essential left socle and rl K s K for every small right ideal K of R, then R is right continuous. Accordingly some well-known classes of rings, such as dual rings and rings all of whose cyclic right R-modules are essentially embedded in projectives, are shown to be continuous. We also prove that a ring R has a perfect duality if and only if the dual of every simple right R-module is simple and R [ R is a left and right CS-module. In Sect. 2 of the paper we provide a characterization for semiperfect right self-injective rings in terms of the CS-condition. ᮊ 1997 Academic Press w x According to S. K. Jain and S. Lopez-Permouth 15 , a ring R is called a ŕight CEP-ring if every cyclic right R-module is essentially embedded in a Ž . projective free right R-module. In a recent and interesting article by J. L. w x Gomez Pardo and P. A. Guil Asensio 9 , right CEP-rings were shown to