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2011

University of Nebraska - Lincoln

Algebra

Local Cohomology

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Annihilators Of Local Cohomology Modules, Laura Lynch Apr 2011

Annihilators Of Local Cohomology Modules, Laura Lynch

Dissertations, Theses, and Student Research Papers in Mathematics

In many important theorems in the homological theory of commutative local rings, an essential ingredient in the proof is to consider the annihilators of local cohomology modules. We examine these annihilators at various cohomological degrees, in particular at the cohomological dimension and at the height or the grade of the defining ideal. We also investigate the dimension of these annihilators at various degrees and we refine our results by specializing to particular types of rings, for example, Cohen Macaulay rings, unique factorization domains, and rings of small dimension.

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