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초록· 키워드
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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
목차
등록된 정보가 없습니다.
참고문헌 (5)
참고문헌 신청
G. Betsch / 1963 / Strukturs¨atze f¨ur Fastringe, Inaugural-Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften der Mathematisch-Naturwissenschaftlichen Fakult"
G. Pilz / 1983 / Near-Rings: The Theory and Its Applications, North-Holland Mathematics Studies, 23 / North-Holland Publishing Co.
M. Holcombe / 1982 / A hereditary radical for near-rings / STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA 17 (1) : 453 ~ 456
S. Veldsman / 1988 / Modulo-constant ideal-hereditary radicals of near-rings / Quaestiones Mathematicae 11 (3) : 253 ~ 278
S. Veldsman / 1989 / On the nonhereditariness of radical and semisimple classes of near-rings / STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA 24 (2) : 315 ~ 323
G. Pilz / 1983 / Near-Rings: The Theory and Its Applications, North-Holland Mathematics Studies, 23 / North-Holland Publishing Co.
M. Holcombe / 1982 / A hereditary radical for near-rings / STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA 17 (1) : 453 ~ 456
S. Veldsman / 1988 / Modulo-constant ideal-hereditary radicals of near-rings / Quaestiones Mathematicae 11 (3) : 253 ~ 278
S. Veldsman / 1989 / On the nonhereditariness of radical and semisimple classes of near-rings / STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA 24 (2) : 315 ~ 323
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