Regularities and Radicals in Near-rings

• 来源期刊: 代数集刊（英文版）
• 关键词: regularity radicals primitive special radicals
• 年，卷（期）: 2002,（3）
• 页码范围: 271-286
• 页数: 16页
• 语种: 英文

摘要

Let F be a regularity for near-rings and F(R) the largest FR-regular ideal in R. In the first part of this paper, we introduce the concepts of maximal Fmodular ideals and F-primitive near-rings to characterize F(R) for any near-ring regularity F. Under certain conditions, F(R) is equal to the intersection of all the maximal F-modular ideals of R. As examples, we apply this to the different analogs of the Brown-McCoy radicals and also the Behrens radicals. In the last part of this paper, we show that for certain regularities, the class of F-primitive near-rings forms a special class.