Abstract
We characterize the second layer condition for a link closed subset of Spec(S) where S is a Noetherian normalizing extension of a Noetherian ring R and R satisfies the second layer condition. The second layer condition is shown to depend on the R-module structure of tame injective S-modules that are naturally associated with prime ideals in the link closed set. This is used to demonstrate that certain twisted polynomial rings satisfy the second layer condition when R is the coefficient ring. In case S is a centralized extension, our characterization is applied to show that the strong second layer condition for S amounts to a diluted version of AR-separation for S whenever R is AR-separated.
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Kosler, K.A. (1997). Normalizing Extensions and the Second Layer Condition. In: Jain, S.K., Rizvi, S.T. (eds) Advances in Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1978-1_16
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DOI: https://doi.org/10.1007/978-1-4612-1978-1_16
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7364-6
Online ISBN: 978-1-4612-1978-1
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