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WEAKLY DUO RINGS WITH NIL JACOBSON RADICAL

이양|Nam Kyun Kim|김홍기
대한수학회 (The Korean Mathematical Society)|2005.05|대한수학회지 (Journal of the KMS)|제42권 제3호|pp. 457-470

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참고문헌

주제분류수학

초록

Abstract

Yu showed that every right (left) primitive factor ring of weakly right (left) duo rings is a division ring. It is not di±cult to show that each weakly right (left) duo ring is abelian and has the classical right (left) quotient ring. In this note we ¯rst pro-vide a left duo ring (but not weakly right duo) in spite of it being left Noetherian and local. Thus we observe conditions under which weakly one-sided duo rings may be two-sided. We prove that a weakly one-sided duo ring R is weakly duo under each of the fol-lowing conditions: (1) R is semilocal with nil Jacobson radical; (2)R is locally ¯nite. Based on the preceding case (1) we study a kind of composition length of a right or left Artinian weakly duo ring R, obtaining that i(R) is ¯nite and ai(R)R = Rai(R) = Rai(R)R for all a 2 R, where i(R) is the index (of nilpotency) of R. Note that one-sided Artinian rings and locally ¯nite rings are strongly ¼-regular. Thus we also observe connections between strongly ¼-regular weakly right duo rings and related rings, constructing avail-able examples.

참고문헌 (17)

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관련 논문AI추천

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