So we see that the classification is quite simple, much like the classification of finite fields, and in strict opposition to the classification of finite simple groups (not to mention the 2023 lack of classification for non simple finite groups!)
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A **finite ring** is a ring that contains a finite number of elements. In more formal terms, a ring \( R \) is an algebraic structure consisting of a set equipped with two binary operations, typically referred to as addition and multiplication, that satisfy certain properties: 1. **Addition**: - \( R \) is an abelian group under addition. This means that: - There exists an additive identity (usually denoted as \( 0 \)).