Another characterization of the upper nil radical

作者：Groenewald N J^*

来源：Acta Mathematica Hungarica, 2016, 150(2): 303-311.

DOI：10.1007/s10474-016-0649-3

• upper radical
• system
• semi-s-prime ideal
• nilprime ideal
• radical

In 2015 Halina France-Jackson introduced the notion of a -ring i.e. a ring R with the property that if I and J are ideals of R and for all , , there exist natural numbers m, n such that , then I = 0 or J = 0. It is shown that is a special class which coincides with the class of all prime nil-semisimple rings. This implies that the upper nil radical of any ring R is the intersection of all ideals I of the ring such that R/I is a -ring. In this paper we introduce classes of rings equivalent to the -rings and then give characterizations of the upper nil radical in terms of these rings.

• 出版日期2016-12