论文信息 - ON WEAK II-REGULARITY AND THE SIMPLICITY OF PRIME FACTOR RINGS

ON WEAK II-REGULARITY AND THE SIMPLICITY OF PRIME FACTOR RINGS

A connection between weak and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

Hai-Lan Jin | Jin Yong Kim

[1] Cui Shun. Some studies on strongly regular rings , 2009 .

[2] G. Birkenmeier,et al. A characterization of minimal prime ideals , 1998, Glasgow Mathematical Journal.

[3] G. Birkenmeier,et al. Regularity conditions and the simplicity of prime factor rings , 1997 .

[4] Victor Camillo,et al. Weakly regular rings , 1994 .

[5] G. Birkenmeier,et al. A connection between weak regularity and the simplicity of prime factor rings , 1994 .

[6] Shuhao Sun. Noncommutative rings in which every prime ideal is contained in a unique maximal ideal , 1991 .

[7] V. Gupta. Weakly π-regular rings and group rings , 1977 .

[8] R. L. Snider,et al. On the von Neumann regularity of rings with regular prime factor rings , 1974 .

[9] Gooyong Shin. Prime ideals and sheaf representation of a pseudo symmetric ring , 1973 .

[10] J. Lambek. On the Representation of Modules by Sheaves of Factor Modules , 1971, Canadian Mathematical Bulletin.

[11] Hans Heinrich Storrer. Epimorphismen von kommutativen Ringen , 1968 .

[12] I. S. Cohen,et al. Commutative rings with restricted minimum condition , 1950 .