In abstract algebra, a **maximal ideal** is a specific type of ideal within a ring. To define it, let's first recall some basic concepts related to rings and ideals: 1. **Ring**: A set equipped with two binary operations, typically called addition and multiplication, satisfying certain properties (like associativity, distributivity, etc.). 2. **Ideal**: A subset of a ring that absorbs multiplication by elements from the ring and is closed under addition.
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