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- W4300664585 abstract "Let $(R, frak m)$ be a local ring and $M$ a finitely generated $R$-module. It is shown that if $M$ is relative Cohen-Macaulay with respect to an ideal $frak a$ of $R$, then $text{Ann}_R(H_{mathfrak{a}}^{text{cd}(mathfrak{a}, M)}(M))=text{Ann}_RM/L=text{Ann}_RM$ and $text{Ass}_R(R/text{Ann}_RM)subseteq {mathfrak{p} in text{Ass}_R M|,{rm cd}(mathfrak{a}, R/mathfrak{p})=text{cd}(mathfrak{a}, M)},$ where $L$ is the largest submodule of $M$ such that ${rm cd}(mathfrak{a}, L)< {rm cd}(mathfrak{a}, M)$. We also show that if $H^{dim M}_{mathfrak{a}}(M)=0$, then $text{Att}_R(H^{dim M-1}_{mathfrak{a}}(M))= {mathfrak{p} in text{Supp} (M)|,{rm cd}(mathfrak{a}, R/mathfrak{p})=dim M-1},$ and so the attached primes of $H^{dim M-1}_{mathfrak{a}}(M)$ depends only on $text{Supp} (M)$. Finally, we prove that if $M$ is an arbitrary module (not necessarily finitely generated) over a Noetherian ring $R$ with ${rm cd}(mathfrak{a}, M)={rm cd}(mathfrak{a}, R/text{Ann}_RM)$, then $text{Att}_R(H^{{rm cd}(mathfrak{a}, M)}_{mathfrak{a}}(M))subseteq{mathfrak{p} in V(text{Ann}_RM)|,{rm cd}(mathfrak{a}, R/mathfrak{p})={rm cd}(mathfrak{a}, M)}.$ As a consequence of this it is shown that if $dim M=dim R$, then $text{Att}_R(H^{dim M}_{mathfrak{a}}(M))subseteq{mathfrak{p} in text{Ass}_R M|,{rm cd}(mathfrak{a}, R/mathfrak{p})=dim M}.$" @default.
- W4300664585 created "2022-10-04" @default.
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- W4300664585 date "2017-07-19" @default.
- W4300664585 modified "2023-10-14" @default.
- W4300664585 title "Some results on the annihilators and attached primes of local cohomology modules" @default.
- W4300664585 doi "https://doi.org/10.48550/arxiv.1707.06536" @default.
- W4300664585 hasPublicationYear "2017" @default.
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