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• W2560005514 abstract "Let R be a commutative ring with <TEX>$1{neq}0$</TEX> and n a positive integer. In this article, we introduce the n-Krull dimension of R, denoted <TEX>$dim_n;R$</TEX>, which is the supremum of the lengths of chains of n-absorbing ideals of R. We study the n-Krull dimension in several classes of commutative rings. For example, the n-Krull dimension of an Artinian ring is finite for every positive integer n. In particular, if R is an Artinian ring with k maximal ideals and l(R) is the length of a composition series for R, then <TEX>$dim_n;R=l(R)-k$</TEX> for some positive integer n. It is proved that a Noetherian domain R is a Dedekind domain if and only if <TEX>$dim_n;R=n$</TEX> for every positive integer n if and only if <TEX>$dim_2;R=2$</TEX>. It is shown that Krull's (Generalized) Principal Ideal Theorem does not hold in general when prime ideals are replaced by n-absorbing ideals for some n > 1." @default.
• W2560005514 created "2016-12-16" @default.
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• W2560005514 date "2016-11-01" @default.
• W2560005514 modified "2023-09-27" @default.
• W2560005514 title "ON n-ABSORBING IDEALS AND THE n-KRULL DIMENSION OF A COMMUTATIVE RING" @default.
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• W2560005514 doi "https://doi.org/10.4134/jkms.j150072" @default.
• W2560005514 hasPublicationYear "2016" @default.
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