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- W4283269124 abstract "Let R be a commutative unitary ring and I an ideal of R. We prove that R+XI[[X]] 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 R[[X]] satisfies ACCd on ideals if and only if R is Noetherian. We deduce that the ring R+XI[[X]] 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." @default.
- W4283269124 created "2022-06-23" @default.
- W4283269124 creator A5002947992 @default.
- W4283269124 date "2022-06-21" @default.
- W4283269124 modified "2023-09-27" @default.
- W4283269124 title "Isonoetherian power series rings III" @default.
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- W4283269124 doi "https://doi.org/10.1080/00927872.2022.2086562" @default.
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