👉 In abstract algebra, a prime ideal is an ideal that is maximal among all ideals containing it. A principal ideal domain (PID) is a ring where every non-zero element has a multiplicative inverse in the ring. The concept of a prime ideal was introduced by Emmy Noether in her study of rings of polynomials over a field. The term "prime" comes from the fact that these ideals are prime in the sense of algebraic number theory, meaning they have no proper factors other than
