A Kurosh-Amitsur left Jacobson radical for right near-rings
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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 J5/2, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that J₂(R) ⊆ J5/2(R) ⊆ J₃(R). It is shown that J5/2 is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But J5/2 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 J5/2 of zero-symmetric near-rings to the class of all 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 J5/2, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that J₂(R) ⊆ J5/2(R) ⊆ J₃(R). It is shown that J5/2 is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But J5/2 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 J5/2 of zero-symmetric near-rings to the class of all near-rings
참고문헌 (5)
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- S. Veldsman, "Modulo-constant ideal-hereditary radicals of near-rings", Quaestiones Mathematicae, 11(3), pp.253~278 (1988)