Algebraic Geometry and Commutative Algebra
In algebraic geometry and commutative algebra, a singularity is a prime ideal whose localization is not a regular local ring (alternately a point of a scheme whose stalk is not a regular local ring). For example, defines an isolated singular point (at the cusp) . The ring in question is given by
The maximal ideal of the localization at is a height one local ring generated by two elements and thus not regular.
Read more about this topic: Mathematical Singularity
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