m-adic perturbations in Noetherian local rings
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The purpose of this thesis is to develop methods for the study m-adic stability in an arbitrary Noetherian local ring. A key role is played by the Artin-Rees lemma. Using these techniques we establish new results about the continuity of Hilbert-Samuel and Hilbert- Kunz multiplicities under m-adic perturbations.
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Ph. D.