A prime ideal is a special type of ideal in a ring that has a crucial role in both algebra and topology. An ideal \( P \) in a ring \( R \) is called prime if whenever the product of two elements is in \( P \), at least one of those elements must also be in \( P \). This property connects prime ideals to the structure of rings and helps in understanding the underlying topology, especially in the context of Boolean algebras.
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