{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86792"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86792","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Some Duality Results in Homological Algebra","abstract":"Finally, we examine local cohomology involving square-free monomial ideals. We provide an alternate proof of one of Mustataˇ's constructions for computing H˙IR and use it to provide a simpler proof of E. Miller's duality result relating H˙IR to H˙m R/I , also showing that the latter result can be expressed in terms of the associated primes of H˙IR and the attached primes of H˙m R/I . To make this work, we prove a fairly general result regarding when the attached primes of a graded module are graded. 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We provide an alternate proof of one of Mustataˇ's constructions for computing H˙IR and use it to provide a simpler proof of E. Miller's duality result relating H˙IR to H˙m R/I , also showing that the latter result can be expressed in terms of the associated primes of H˙IR and the attached primes of H˙m R/I . To make this work, we prove a fairly general result regarding when the attached primes of a graded module are graded. We also investigate purely set-theoretic techniques for computing the local cohomology modules without recourse to linear algebra or symplectic geometry; these techniques can (when applicable) greatly improve computation time.","Made available in DSpace on 2015-09-28T15:19:34Z (GMT). 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We provide an alternate proof of one of Mustataˇ's constructions for computing H˙IR and use it to provide a simpler proof of E. Miller's duality result relating H˙IR to H˙m R/I , also showing that the latter result can be expressed in terms of the associated primes of H˙IR and the attached primes of H˙m R/I . To make this work, we prove a fairly general result regarding when the attached primes of a graded module are graded. We also investigate purely set-theoretic techniques for computing the local cohomology modules without recourse to linear algebra or symplectic geometry; these techniques can (when applicable) greatly improve computation time.","Made available in DSpace on 2015-09-28T15:19:34Z (GMT). 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