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8.1: Definitions and Examples
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Recall that a group is a set together with a single binary operation, which together satisfy a few modest properties. Loosely speaking, a ring is a set together with two binary operations (called addition and multiplication) that are related via a distributive property.
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8.2: Ring Homomorphisms
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8.3: Ideals and Quotient Rings
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8.4: Maximal and Prime Ideals
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In this section of notes, we will study two important classes of ideals, namely maximal and prime ideals, and study the relationship between them. Throughout this entire section, we assume that all rings have a multiplicative identity 1≠0 .