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http://dx.doi.org/10.5666/KMJ.2014.54.4.595

Special Right Jacobson Radicals for Right Near-rings  

Rao, Ravi Srinivasa (Department of Mathematics, R. V. R. & J. C. College of Engineering)
Prasad, Korrapati Siva (Department of Mathematics, Acharya Nagarjuna University)
Publication Information
Kyungpook Mathematical Journal / v.54, no.4, 2014 , pp. 595-606 More about this Journal
Abstract
In this paper three more right Jacobson-type radicals, $J^r_{g{\nu}}$, are introduced for near-rings which generalize the Jacobson radical of rings, ${\nu}{\in}\{0,1,2\}$. It is proved that $J^r_{g{\nu}}$ is a special radical in the class of all near-rings. Unlike the known right Jacobson semisimple near-rings, a $J^r_{g{\nu}}$-semisimple near-ring R with DCC on right ideals is a direct sum of minimal right ideals which are right R-groups of type-$g_{\nu}$, ${\nu}{\in}\{0,1,2\}$. Moreover, a finite right $g_2$-primitive near-ring R with eRe a non-ring is a near-ring of matrices over a near-field (which is isomorphic to eRe), where e is a right $g_2$-primitive idempotent in R.
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