期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2008
卷号：2008
DOI：10.1155/2008/741609
出版社：Hindawi Publishing Corporation
摘要：By a near-ring we mean a right near-ring. 𝐽𝑟0, the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radical 𝐽𝑟0
are studied. It is shown that 𝐽𝑟0 is a Kurosh-Amitsur radical (KA-radical) in the variety of all near-rings
𝑅, in which the constant part 𝑅𝑐
of 𝑅
is an ideal of 𝑅. So unlike the left Jacobson radicals of types 0 and 1 of near-rings, 𝐽𝑟0 is a KA-radical in the class of all zero-symmetric near-rings. 𝐽𝑟0 is not 𝑠-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.
