Section: Ideals
Ideals are special subsets of rings, which are closed under the addition operation an absorb other elements of the ring, when multiplied by elements of the ideal. As an example, the set \(E\) of even numbers in the ring \((\mathbb Z, + ,\cdot)\) constitutes an ideal, since the addition and subtraction of any two even numbers preserves evenness, and multiplying any (even or odd) integer by an even number also creates an even number.
Table of Contents
 Definition: Ideal
 Proposition: Principal Ideals being Prime Ideals
 Proposition: Principal Ideals being Maximal Ideals
 Definition: Principal Ideal
 Definition: Generating Set of an Ideal
 Definition: Prime Ideal
 Definition: Maximal Ideal
 Lemma: Prime Ideals of Multiplicative Systems in Integral Domains
 Theorem: Connection between Rings, Ideals, and Fields
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Chapters: 1
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