prime ideal
prime ideal · prime ideals
Any ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆IAny (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
Meaning
2 sensesAny (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
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.
Translations
2 languagesOrigin
By analogy with the notion of prime number in number theory.By analogy with the notion of prime number in number theory.
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Forms
plural: prime ideals| Singular | prime ideal |
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| Plural | prime ideals |
regular