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Homology of artinian modules over commutative noetherian rings

Micah Josiah Leamer, University of Nebraska - Lincoln

Abstract

This work is primarily concerned with the study of artinian modules over commutative noetherian rings.^ We start by showing that many of the properties of noetherian modules that make homological methods work seamlessly have analogous properties for artinian modules. We prove many of these properties using Matlis duality and a recent characterization of Matlis reflexive modules. Since Matlis reflexive modules are extensions of noetherian and artinian modules many of the properties that hold for artinian and noetherian modules naturally follow for Matlis reflexive modules and more generally for mini-max modules.^ In the last chapter we prove that if the Betti numbers of a finitely generated module over an equidimensional local ring are eventually non-decreasing, then the dimensions of sufficiently high syzygies are constant. ^

Subject Area

Mathematics

Recommended Citation

Leamer, Micah Josiah, "Homology of artinian modules over commutative noetherian rings" (2011). ETD collection for University of Nebraska - Lincoln. AAI3450090.
http://digitalcommons.unl.edu/dissertations/AAI3450090

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