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Abstract:
A closure operation is an idempotent endomorphism on the set of ideals
of a given ring, which produces an ideal that contains the given
ideal, and preserves containment of ideals. If defined element-wise,
a closure operation can be seen as a necessary condition for
membership in an ideal. I will discuss various closure operations
(e.g. radical, integral closure, saturation, continuous closure), as
well as some of their properties and how they arise. |