prime ideal
nounEtymology
By analogy with the notion of prime number in number theory.
Definitions
Any (two-sided) ideal I such that for arbitrary ideals P and Q, PQ⊆I⟹P⊆I or Q⊆I.
- Given a prime number p, there is only a finite number of prime ideals #92;mathfrak#123;p#125; in #92;mathfrak#123;o#125; such that #92;mathfrak#123;p#125;#92;capJ#61;p (they are the prime ideals of #92;mathfrak#123;o#125;p).
In a commutative ring, a (two-sided) ideal I such that for arbitrary ring elements a and…
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.
The neighborhood
Vish — recursive loop
No curated loop yet for prime ideal. Loops are being traced one word at a time while the ingestion pipeline matures.
sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA