Commutative reduced filial rings

Ryszard R. Andruszkiewicz, Magdalena Sobolewska

Abstract


A ring \(R\) is filial when for every \(I\), \(J\), if \(I\) is an ideal of \(J\) and \(J\) is an ideal of \(R\) then \(I\) is an ideal of \(R\). Several characterizations and results on structure of commutative reduced filial rings are obtained.


Keywords


ideal, filial ring, reduced ring

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