ADE Classification of Hypersurface Singularities over Local Rings

Abstract: In this paper we present an ADE-type classification of hypersurfaces of complete regular local rings based on their Cohen-Macaulay type. In order to preform this classification, we show how we can generalize the classical result regarding finite and countable Cohen-Macaulay type to larger cardinalities, depending on the cardinality of the residue field.