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Local Cohomology ModulesVertex SetLocal CohomologyCommutative Ring with IdentityCommutative Noetherian RingLocal RingTriangular Matrix RingsFixed PointsLow-density Parity-checkNecessary and Sufficient ConditionMaximal FilterNoetherian Local RingExponent MatrixCohomological DimensionGeneralized Local Cohomology ModuleAssociative RingStrongly Regular RelationsHausdorff SpaceCirculant Permutation MatricesAlgebraic Structures