prime ideal (English, noun)
expansion: prime ideal (plural prime ideals)
Senses:
topics: algebra
mathematics
sciences
qualifier: ring theory
glosses: Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
glosses: 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.
Forms:
form: prime ideals
tags: plural