query: Primary ideals are those whose quotient has irreducible prime spectrum.
positive_passages.docid: 16593
positive_passages.text: Irreducible Spectrum implies Zero-Divisors are Nilpotent
negative_passages.docid: 17247
negative_passages.text: Localisation and prime ideals
negative_passages.docid: 110022
negative_passages.text: Showing prime and maximal ideal
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 111935
negative_passages.text: Irreducible but not prime
negative_passages.docid: 138882
negative_passages.text: A prime poset of ideals
negative_passages.docid: 87103
negative_passages.text: Quick question about ideals of field $F$ in $F[x]$ are principal.
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 59411
negative_passages.text: Primary ideals confusion with definition
negative_passages.docid: 108896
negative_passages.text: Prime ideal in a polynomial ring over an integrally closed domain
negative_passages.docid: 151829
negative_passages.text: Why are maximal ideals prime?
negative_passages.docid: 149747
negative_passages.text: Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
negative_passages.docid: 120147
negative_passages.text: For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
negative_passages.docid: 65536
negative_passages.text: Finitely generated ideals in a Boolean ring are principal, why?
negative_passages.docid: 60223
negative_passages.text: Two principal ideals coincide if and only if their generators are associated
negative_passages.docid: 70047
negative_passages.text: Is the ideal generated by irreducible element in principal ideal domain maximal?