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- W3041853721 abstract "Assume that (R) is a complete Noetherian local ring and (M) is a non-zero finitely generated (R)-module of dimension (n=dim(M)geq 1). It is shown that any non-empty subset (T) of (mathrm{Assh}(M)) can be expressed as the set of attached primes of the top local cohomology modules (H_{I,J}^n(M)) for some proper ideals (I,J) of (R). Moreover, for ideals (I, J=bigcap_ {mathfrak pin mathrm{Att}_R(H_{I}^n(M))}mathfrak p) and (J') of (R) it is proved that (T=mathrm{Att}_R(H_{I,J}^n(M))=mathrm{Att}_R(H_{I,J'}^n(M))) if and only if (J'subseteq J). Let (H_{I,J}^n(M)neq 0). It is shown that there exists (Qin mathrm{Supp}(M)) such that (dim(R/Q)=1) and (H_Q^n(R/{mathfrak p})neq 0), for each (mathfrak p in mathrm{Att}_R(H_{I,J}^n(M))). In addition, we prove that if (I) and (J) are two proper ideals of a Noetherian local ring (R), then (mathrm{Ann}_R(H_{I,J}^{n}(M))=mathrm{Ann}_R(M/{T_R(I,J,M)})), where (T_R(I,J,M)) is the largest submodule of (M) with (mathrm{cd}(I,J,T_R(I,J,M))<mathrm{cd}(I,J,M)), here (mathrm{cd}(I,J,M)) is the cohomological dimension of (M) with respect to (I) and (J). This result is a generalization of [1, Theorem 2.3] and [2, Theorem 2.6]." @default.
- W3041853721 created "2020-07-16" @default.
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- W3041853721 date "2020-01-01" @default.
- W3041853721 modified "2023-09-24" @default.
- W3041853721 title "Attached primes and annihilators of top local cohomology modules defined by a pair of ideals" @default.
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- W3041853721 doi "https://doi.org/10.12958/adm429" @default.
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