论文信息 - On Rings Whose Strongly Prime Ideals Are Completely Prime

On Rings Whose Strongly Prime Ideals Are Completely Prime

Kaplansky introduced the concept of the K-rings, concerning the commutativity of rings. In this paper, we concentrate on a property of K-rings, introducing the concept of the strongly NI rings, which is stronger than NI-ness. We first examine the relations among the concepts concerned with K-rings and strongly NI rings, constructing necessary examples in the process. We also show that strong NI-ness is a hereditary radical property.

[1] A. Smoktunowicz. Polynomial Rings over Nil Rings Need Not Be Nil , 2000 .

[2] J. Ram. On the semisimplicity of skew polynomial rings , 1984 .

[3] Yang Lee,et al. Questions on 2-primal rings , 1998 .

[4] T. Kwak,et al. On minimal strongly prime ideals , 2000 .

[5] Yang Lee,et al. An Ascending Chain Condition on Wedderburn Radicals , 2006 .

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

[7] Ken R. Goodearl,et al. An Introduction to Noncommutative Noetherian Rings , 1989 .

[8] G. Marks. ON 2-PRIMAL ORE EXTENSIONS , 2001 .

[9] I. Kaplansky. A Theorem on Division Rings , 1951, Canadian Journal of Mathematics.

[10] Yang Lee,et al. On rings whose prime ideals are completely prime , 2002 .

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

[12] Yang Lee,et al. Weakly regular rings with ACC on annihilators and maximality of strongly prime ideals of weakly regular rings , 2006 .

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

[14] Yang Lee,et al. Structure and topological conditions of NI rings , 2006 .

[15] Tsit Yuen Lam,et al. A first course in noncommutative rings , 2002 .