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Let (R, m) be a Noetherian local ring, I an ideal of R and N a finitely generated R-module. Let k≥ − 1 be an integer and r = depth k (I, N) the length of a maximal N-sequence in dimension \u003e k in I defined by M. Brodmann and L. T. Nhan (Comm. Algebra, 36 (2008), 1527-1536). For a subset S ⊆ Spec R we set S ≥k = {p ∈ S | dim(R/p)≥k}. We first prove in this paper that Ass R (H j I (N)) ≥k is a finite set for all j≤r. Let N = ⊕ n≥0 N n be a finitely generated graded R-module, where R is a finitely generated standard graded algebra over R 0 = R. Let r be the eventual value of depth k (I, N n). Then our second result says that for all l≤r the sets j≤l Ass R (H j I (N n)) ≥k are stable for large n.","publication_date":"2013,,","publication_name":"Communications in Algebra","grobid_abstract_attachment_id":"96866595"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On The Finiteness and Stability of Certain Sets of Associated Prime Ideals of Local Cohomology Modules","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [252120497]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loswp.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div 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Let t be a non-negative integer. In this paper, it is shown that [Formula: see text] for all i &lt; t if and only if there exists an ideal 𝔟 of R such that dim R/𝔟 ≤ 1 and [Formula: see text] for all i &lt; t. 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