Principal Ideal Domain

A Principal Ideal Domain (PID) is a type of mathematical structure within algebra, specifically a ring, where every ideal (a special subset) can be generated by a single element. Think of it like a system where all sub-collections follow a simple rule: each can be created by multiplying a single, specific element. This property simplifies the understanding of divisibility and factorization within the system, making PIDs key in areas like number theory and algebra. Examples include the integers and certain polynomial rings, where the well-behaved structure facilitates solving equations and studying divisibility.