KnowraIdealLinked fromLinked fromThe 11 pages that link to Ideal, each with the reason it gives.All 11Broader topic 3Related 3Narrower topic 5Algebraic number theoryBroader topic: Ideals restore unique factorization in settings where elements do not factor uniquely.Prime idealNarrower topic: Primality is an additional condition imposed on an ideal.Quotient ringNarrower topic: The chosen ideal determines which elements become equivalent in the quotient.Maximal idealNarrower topic: Maximality compares an ideal with every larger ideal in the same ring.Commutative algebraRelated: Ideals encode equations, quotient rings, and geometric subspaces.Bézout's identityRelated: In the integers, the ideal generated by a and b consists of their linear combinations and equals the ideal generated by their gcd.Algebraic number fieldRelated: Ideals allow factorization to remain useful when elements do not factor uniquely.Hilbert's basis theoremNarrower topic: The theorem's conclusion concerns finite generation of every ideal in the polynomial ring.Ring theoryBroader topic: Ideals identify subsets that can be collapsed while preserving ring operations.Artin–Rees lemmaNarrower topic: Its powers define the filtration whose induced behavior the theorem constrains.Krull's theoremBroader topic: The theorem orders proper ideals by inclusion to find one maximal among them.