A Kurosh-Amitsur left Jacobson radical for right near-rings
Bull. Korean Math. Soc. 2008 Vol. 45, No. 3, 457-466
Published online September 1, 2008
Ravi Srinivasa Rao and K. Siva Prasad
P. B. Siddhartha College of Arts and Science, Chalapathi Institute of Engineering and Technology
Abstract : Let $R$ be a right near-ring. An $R$-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An $R$-group of type-5/2 is an $R$-group of type-2 and an $R$-group of type-3 is an $R$-group of type-5/2. Using it J$_{5/2}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that J$_{2}$$(R)$ $\subseteq$ J$_{5/2}$$(R)$ $\subseteq$ J$_{3}$$(R)$. It is shown that J$_{5/2}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But J$_{5/2}$ is not a KA-radical in the class of all near-rings. By introducing an $R$-group of type-(5/2)(0) it is shown that J$_{(5/2)(0)}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical J$_{5/2}$ of zero-symmetric near-rings to the class of all near-rings.
Keywords : near-ring, $R$-groups of type-5/2 and (5/2)(0), Jacobson radicals of type-5/2 and (5/2)(0)
MSC numbers : 16Y30
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