Beiträge zur Algebra und GeometrieContributions to Algebra and Geometry
Vol. 50, No. 1, pp. 11-23 (2009)
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Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 11-23 (2009) |
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Hereditary right Jacobson radical of type-0($e$) for right near-ringsRavi Srinivasa Rao, K. Siva Prasad and T. SrinivasDepartment of Mathematics, P. G. Centre, P. B. Siddhartha College of Arts and Science, Vijayawada-520010, Andhra Pradesh, Indiae-mail: dr_rsrao@@yahoo.com; Department of Mathematics, Chalapathi Institute of Engineering and Technology Chalapathi Nagar, Lam, Guntur-522034, Andhra Pradesh, India; Department of Mathematics, Kakatiya University Warangal-506009, Andhra Pradesh, India Abstract: Near-rings considered are right near-rings and R is a near-ring. The first two authors introduced right Jacobson radicals of type-0, 1 and 2 for right near-rings. Recently, the authors have shown that these right Jacobson radicals are Kurosh-Amitsur radicals (KA-radicals) in the class of all zero-symmetric near-rings but they are not ideal-hereditary in that class. In this paper right R-groups of type-0(e), right 0(e)-primitive ideals and right 0(e)-primitive near-rings are introduced. Using them the right Jacobson radical of type-0(e) is introduced for near-rings 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 KA-radical in the class of all near-rings and is an ideal-hereditary radical in the class of all zero-symmetric near-rings. Keywords: right R-group of type-$0(e)$, right 0(e)-primitive ideal, right Jacobson radical of type-$0(e)$, KA-radical, hereditary radical Classification (MSC2000): 16Y30 Full text of the article:
Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.
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