Finitely generated refers to a property of an algebraic object, typically a module or an algebra, where it can be constructed from a finite set of generators. This concept is essential in various areas of mathematics, including algebraic geometry, as it relates to the structure and behavior of algebraic varieties and their singularities. Understanding whether an algebraic object is finitely generated can provide insights into its dimensionality and complexity, which are critical when analyzing canonical and terminal singularities.
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