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