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2012•Unpublished venueOpen access

A Guide to Closure Operations in Commutative Algebra

Neil Epstein

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Abstract

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part.The survey is broad enough to encompass the radical, tight closure, integral closure, basically full closure, saturation with respect to a fixed ideal, and the v-operation, among others.

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This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part.The survey is broad enough to encompass the radical, tight closure, integral closure, basically full closure, saturation with respect to a fixed ideal, and the v-operation, among others.

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OpenAlex reports 33 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part.The survey is broad enough to encompass the radical, tight closure, integral closure, basically full closure, saturation with respect to a fixed ideal, and the v-operation, among others.

Key concepts: Closure (psychology), Algebra over a field, Commutative property, Computer science, Mathematics, Pure mathematics, Political science, Law

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