A prime ideal is a special type of ideal in the field of abstract algebra, particularly in ring theory. An ideal is a subset of a ring that absorbs multiplication by elements of the ring. A prime ideal has the property that if the product of two elements from the ring is in the ideal, then at least one of those elements must also be in the ideal. Prime ideals play a crucial role in the structure of rings and are closely related to prime numbers in number theory. They help in understanding the factorization of elements within a ring and are essential in defining integral domains and fields.