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• W2053209657 abstract "Let G be a group acting via ring automorphisms on a commutative unital ring R. If Spec(R) has no infinite antichains and either R a domain or G finitely generated, then R G  ⊆ R has the lying-over property. If R is semiquasilocal and dim(R) = 0, then dim(R G ) = 0. If 1 ≤ d ≤ ∞, new examples are given such that d = dim(R) ≠ dim(R G ) < ∞. If G is locally finite on R, then R G  ⊆ R satisfies universally going-down. Consequently, if G is locally finite, the S-domain, strong S-domain and universally strong S-domain properties descend from R to R G . If R is a domain, then G is locally finite on R ⇔ R is integral over R G . One cannot delete the “domain” hypothesis." @default.
• W2053209657 created "2016-06-24" @default.
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• W2053209657 date "2007-04-13" @default.
• W2053209657 modified "2023-09-23" @default.
• W2053209657 title "Transfer of Krull Dimension, Lying-Over, and Going-Down to the Fixed Ring" @default.
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• W2053209657 doi "https://doi.org/10.1080/00927870601142231" @default.
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