Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings

By a near-ring we mean a right near-ring. J0r, 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 J0r are studied. It is shown that J0r is a Kurosh-Amitsur radical (KA-radical) in the variety of all near-rings...

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Main Authors: Ravi Srinivasa Rao, K. Siva Prasad, T. Srinivas
Format: Article
Language:English
Published: Wiley 2008-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2008/741609
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author Ravi Srinivasa Rao
K. Siva Prasad
T. Srinivas
author_facet Ravi Srinivasa Rao
K. Siva Prasad
T. Srinivas
author_sort Ravi Srinivasa Rao
collection DOAJ
description By a near-ring we mean a right near-ring. J0r, 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 J0r are studied. It is shown that J0r 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, J0r is a KA-radical in the class of all zero-symmetric near-rings. J0r is not s-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-a58bd914b9ce49fb8d556955cbf7e5812025-08-20T02:20:37ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/741609741609Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-RingsRavi Srinivasa Rao0K. Siva Prasad1T. Srinivas2Department of Mathematics, P.G.Centre, P.B. Siddhartha College of Arts and Science, Vijayawada-520010, Andhra Pradesh, IndiaDepartment of Mathematics, Chalapathi Institute of Engineering and Technology, Chalapathi Nagar, Lam, Guntur-522034, Andhra Pradesh, IndiaDepartment of Mathematics, Kakatiya University, Warangal-506009, Andhra Pradesh, IndiaBy a near-ring we mean a right near-ring. J0r, 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 J0r are studied. It is shown that J0r 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, J0r is a KA-radical in the class of all zero-symmetric near-rings. J0r is not s-hereditary and hence not an ideal-hereditary radical in the class of all zero-symmetric near-rings.http://dx.doi.org/10.1155/2008/741609
spellingShingle Ravi Srinivasa Rao
K. Siva Prasad
T. Srinivas
Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
International Journal of Mathematics and Mathematical Sciences
title Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
title_full Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
title_fullStr Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
title_full_unstemmed Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
title_short Kurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
title_sort kurosh amitsur right jacobson radical of type 0 for right near rings
url http://dx.doi.org/10.1155/2008/741609
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