- A Study on Near-rings with SR-Conditions
- 조용욱 ;
- Kyungpook mathematical journal, volume 41, issue 1, 2001, Pages 29~29
Abstract
In 1980, G. Mason introduced the notions of left strong regularity, right strong regularity, left regularity and right regularity. He proved that for a zero symmetric unital near-rings, the notions of left strong regularity, left regularity and right regularity are equivalent. In 1984, the properties of stong regularity have been slightly improved by C. V. L. N. Murty and also in 1986, that of strong regularity and strong π-regularity of semi-groups were investigated by M. Hongan. Our first aim of this paper is to investigate some characterization of left strongly regularity of near-rings, that is, the four concepts of left strong regurality, left s-unital and left bipotent, reduced and left bipotent, and regurality with some condition are all equivalent under zero symmetric near-ring. Next, we will define some concepts of near-rings: SR-conditions, right semi-centrality, generalized left bipotent and generalized right bipotent. Our second aim is to prove that the notions of π-regurality and strong π-regularity are equivalent under SR-conditions, and under GLB, those of left strong regularity and right strong regularity are equivalent.