Abstract
The notions of a right quasiregular element and right modular right ideal in a near-ring are initiated. Based on theseJ0r(R), the right Jacobson radical of type-0 of a near-ringRis introduced. It is obtained thatJ0ris a radical map andN(R)⊆J0r(R), whereN(R)is the nil radical of a near-ringR. Some characterizations ofJ0r(R) are given and its relation with some of the radicals is also discussed.
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