Abstract
Let R be a commutative unitary ring and I an ideal of R. We prove that is isonoetherian if and only if R is isonoetherian, I is idempotent and each ideal of R contained in I is finitely generated. We prove that satisfies ACC d on ideals if and only if R is Noetherian. We deduce that the ring satisfies ACC d on ideals if and only if R satisfies ACC d on ideals, I is idempotent and each ideal of R contained in I is finitely generated. We study polynomial rings satisfying ACC d on ideals. We give an example of a ring satisfying ACC d on ideals but is not isonoetherian.
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