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- W3091570538 abstract "Let $$mathfrak{a}$$ be an ideal of Noetherian ring R and M a finitely generated R-module. In this paper we determine $${rm{An}}{{rm{n}}_R}({rm{H}}_{mathfrak{a}}^{{rm{cd}}(mathfrak{a},M)}(M))$$ and $${rm{At}}{{rm{t}}_R}({rm{H}}_{mathfrak{a}}^{{rm{cd}}(mathfrak{a},M)}(M))$$, which are two important problems concerning the last nonzero local cohomology module $${rm{H}}_{mathfrak{a}}^{{rm{cd}}(mathfrak{a},M)}(M)$$. We show that $${rm{An}}{{rm{n}}_R}({rm{H}}_{mathfrak{a}}^{{rm{cd}}(mathfrak{a},M)}(M)) = {rm{An}}{{rm{n}}_R}(M/{T_R}(mathfrak{a},M))$$, where $${T_R}(mathfrak{a},M)$$ is the largest submodule of M such that $${rm{cd}}(mathfrak{a},{T_R}(mathfrak{a},M)) < {rm{cd}}(mathfrak{a},M)$$. Using the above result we determine the attached primes of the top local cohomology module $${rm{At}}{{rm{t}}_R}({rm{H}}_{mathfrak{a}}^{{rm{cd}}(mathfrak{a},M)}(M))$$. In fact, we show that $${rm{At}}{{rm{t}}_R}({rm{H}}_{mathfrak{a}}^{{rm{cd}}(mathfrak{a},M)}(M)) = left{ {mathfrak{p} in {rm p }{{rm{p}}_R}M:;{rm{cd}}(mathfrak{a},;R/mathfrak{p}) = {rm{cd}}(mathfrak{a},M)} right}$$. Then by using these, we obtain some main results of A. Atazadeh, M. Sedghi, R. Naghipour (2014), K. Bahmanpour, J. A’zami, G. Ghasemi (2012) and K. Divaani-Aazar (2009)." @default.
- W3091570538 created "2020-10-08" @default.
- W3091570538 creator A5046454851 @default.
- W3091570538 date "2020-05-05" @default.
- W3091570538 modified "2023-10-12" @default.
- W3091570538 title "Retracted article: Annihilators and attached primes of top local cohomology modules" @default.
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- W3091570538 doi "https://doi.org/10.21136/cmj.2020.0479-19" @default.
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