English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, at first, we show that for a ramified regular local ring $S$,which is an Eisenstein extension of an unramified regular local ring $R$, whenan ideal $I$ of $S$ is extended from an ideal $J$ of $R$, the puncturedspectrum of $R/J$ is connected if that of $S/JS$ is connected. Using this, weextend the result of SVT to complete ramified regular local ring only for theextended ideals. If the punctured spectrum of $S/JS$ is disconnected then thatof $R/J$ is also disconnected when every minimal primes $\p$ of $J$, $R/\p$ isnormal. Under this situation we prove that both of them have the same number ofconnected components and the Matlis duals of the local cohomology modulessupport the Conjecture 1 and the result of Corollary 1.2 of \cite{L-Y}.

Eisenstein extension, connectedness and the second vanishing theorem