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- W2273924156 abstract "For a Noetherian regular ring $S$ and for a fixed ideal $Jsubset S$, assume that the associated primes of local cohomology module $H^i_J(S)$ does not contain $p$ for some $igeq 0$, 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 Noetherian regular local ring $S$ and for a fixed ideal $Jsubset S$, associated primes of local cohomology module $H^i_J(S)$ for $igeq 0$ is finite, if it does not contain $p$. In this paper, we study how the property $textit{textbf{P}}$ (as mentioned above) can come down from unramified regular ring to ramified regular local ring. In cite{SW}, Bockstein homomorphism is studied in the context to the finiteness of associated primes of local cohomology modules for the ring of integers. There it is shown that if $p$ is nonzero divisor of Koszul homology then Bockstein homomorphism is a zero map (see, Theorem 3.1 of cite{SW}). Here, in this paper, as a consequence of property $textit{textbf{P}}$, we extend the result of Theorem 3.1 of cite{SW} to the ramified regular local ring." @default.
- W2273924156 created "2016-06-24" @default.
- W2273924156 creator A5090417074 @default.
- W2273924156 date "2015-12-17" @default.
- W2273924156 modified "2023-09-27" @default.
- W2273924156 title "A Note on Associated Primes and Bockstein Homomorphisms of Local Cohomology Modules for Ramified Regular Local Rings" @default.
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