Ideal theory
Theory of ideals in commutative rings in mathematics / From Wikipedia, the free encyclopedia
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This article is about the mathematical theory. For the usage in political philosophy, see Ideal theory (politics).
In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more substantial theory exists only for commutative rings (and this article therefore only considers ideals in commutative rings.)
Throughout the articles, rings refer to commutative rings. See also the article ideal (ring theory) for basic operations such as sum or products of ideals.