In mathematics, the Lasker–Noether theorem states that every Noetherian ring is a Lasker ring, which means that every ideal can be decomposed as an intersection, called primary decomposition, of finitely many primary ideals (which are related to, but not quite the same as, powers of prime ideals). The theorem was first proven by EmanuelLasker (1905) for the special case of polynomial rings and convergent power series rings, and was proven in its full generality by EmmyNoether (1921).