For questions about prime ideals and maximal ideals in rings.

In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. They are defined as ideals such that $ab\in I$ implies $a\in I$ or $b\in I$. A maximal ideal ideal is an ideal which is maximal w.r.t. inclusion.

In the ring of integers maximal and prime ideals coincide. They are the sets that contain all the multiples of a given prime number, together with the zero ideal.