prime ideal

Short definition from Wiktionary

Noun

1. 1
   Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
2. 2
   In a commutative ring, a (two-sided) ideal I such that for arbitrary ring elements a and b, ab∈I⟹a∈I or b∈I.