Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 1123 (2009) 

Hereditary right Jacobson radical of type0($e$) for right nearringsRavi Srinivasa Rao, K. Siva Prasad and T. SrinivasDepartment of Mathematics, P. G. Centre, P. B. Siddhartha College of Arts and Science, Vijayawada520010, Andhra Pradesh, Indiaemail: dr_rsrao@@yahoo.com; Department of Mathematics, Chalapathi Institute of Engineering and Technology Chalapathi Nagar, Lam, Guntur522034, Andhra Pradesh, India; Department of Mathematics, Kakatiya University Warangal506009, Andhra Pradesh, India Abstract: Nearrings considered are right nearrings and R is a nearring. The first two authors introduced right Jacobson radicals of type0, 1 and 2 for right nearrings. Recently, the authors have shown that these right Jacobson radicals are KuroshAmitsur radicals (KAradicals) in the class of all zerosymmetric nearrings but they are not idealhereditary in that class. In this paper right Rgroups of type0(e), right 0(e)primitive ideals and right 0(e)primitive nearrings are introduced. Using them the right Jacobson radical of type0(e) is introduced for nearrings and is denoted by J$^{r}_{0(e)}$. A right 0(e)primitive ideal of R is an equiprime ideal of R. It is shown that J$^{r}_{0(e)}$ is a KAradical in the class of all nearrings and is an idealhereditary radical in the class of all zerosymmetric nearrings. Keywords: right Rgroup of type$0(e)$, right 0(e)primitive ideal, right Jacobson radical of type$0(e)$, KAradical, hereditary radical Classification (MSC2000): 16Y30 Full text of the article:
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