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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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| 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. |
| format | Article |
| id | doaj-art-a58bd914b9ce49fb8d556955cbf7e581 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT ravisrinivasarao kuroshamitsurrightjacobsonradicaloftype0forrightnearrings AT ksivaprasad kuroshamitsurrightjacobsonradicaloftype0forrightnearrings AT tsrinivas kuroshamitsurrightjacobsonradicaloftype0forrightnearrings |