query: Why principal ideals in Z[x] are not maximal?
positive_passages.docid: 17991
positive_passages.text: Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
negative_passages.docid: 65536
negative_passages.text: Finitely generated ideals in a Boolean ring are principal, why?
negative_passages.docid: 43103
negative_passages.text: Unique factorization domain and principal ideals
negative_passages.docid: 68202
negative_passages.text: Must an ideal generated by an irreducible element be a maximal ideal?
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 81743
negative_passages.text: Prime ideals in $C[0,1]$
negative_passages.docid: 121986
negative_passages.text: Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
negative_passages.docid: 60674
negative_passages.text: Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
negative_passages.docid: 138114
negative_passages.text: Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
negative_passages.docid: 75899
negative_passages.text: Principal ideal domain with finitely many ideals
negative_passages.docid: 118306
negative_passages.text: $I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
negative_passages.docid: 113152
negative_passages.text: Prove Principal Ideal Domain from Bezout's condition, and terminating divisibility chain
negative_passages.docid: 6646
negative_passages.text: A (non-artificial) example of a ring without maximal ideals
negative_passages.docid: 87780
negative_passages.text: Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
negative_passages.docid: 84663
negative_passages.text: $A$ local Noetherian ring with principal maximal ideal implies PIR?