A KUROSH-AMITSUR LEFT JACOBSON RADICAL FOR RIGHT NEAR-RINGS

Title & Authors
A KUROSH-AMITSUR LEFT JACOBSON RADICAL FOR RIGHT NEAR-RINGS

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 $\small{J_{5/2}}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that $\small{J_2(R){\subseteq}J_{5/2}(R){\subseteq}J_3(R)}$. It is shown that $\small{J_{5/2}}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But $\small{J_{5/2}}$ 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 $\small{J_{(5/2)(0)}}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical $\small{J_{5/2}}$ 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);
Language
English
Cited by
References
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