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

For a Noetherian regular ring $S$ and for a fixed ideal $J\subset S$, assumethat the associated primes of local cohomology module $H^i_J(S)$ does notcontain $p$ for some $i\geq 0$, and we call this as a property$\textit{\textbf{P}}^{i,p}_{J,S}$ or $\textit{\textbf{P}}$ for brevity.Recently, in Theorem 1.2 of \cite{Nu1}, it is proved that in a Noetherianregular local ring $S$ and for a fixed ideal $J\subset S$, associated primes oflocal cohomology module $H^i_J(S)$ for $i\geq 0$ is finite, if it does notcontain $p$. In this paper, we study how the property $\textit{\textbf{P}}$ (asmentioned above) can come down from unramified regular ring to ramified regularlocal ring. In \cite{SW}, Bockstein homomorphism is studied in the context tothe finiteness of associated primes of local cohomology modules for the ring ofintegers. There it is shown that if $p$ is nonzero divisor of Koszul homologythen Bockstein homomorphism is a zero map (see, Theorem 3.1 of \cite{SW}).Here, in this paper, as a consequence of property $\textit{\textbf{P}}$, weextend the result of Theorem 3.1 of \cite{SW} to the ramified regular localring.

A Note on Associated Primes and Bockstein Homomorphisms of Local Cohomology Modules for Ramified Regular Local Rings