query: A maximal ideal is not contained in the union of all the other maximals ideals
positive_passages.docid: 154239
positive_passages.text: Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
negative_passages.docid: 112045
negative_passages.text: A property of minimal prime ideal
negative_passages.docid: 134991
negative_passages.text: Commutative non Noetherian rings in which all maximal ideals are finitely generated
negative_passages.docid: 28629
negative_passages.text: Is the axiom of choice necessary to prove that closed points in the Zariski topology are maximal ideals?
negative_passages.docid: 6646
negative_passages.text: A (non-artificial) example of a ring without maximal ideals
negative_passages.docid: 17991
negative_passages.text: Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
negative_passages.docid: 107463
negative_passages.text: Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
negative_passages.docid: 151786
negative_passages.text: Proving that there is no ideal $I$ in $\mathbb{Z}[t]$ such that $\mathbb{Z}[t]/I \cong \mathbb{Q}$
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 87382
negative_passages.text: Non-invertible elements form an ideal
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals
negative_passages.docid: 49521
negative_passages.text: In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
negative_passages.docid: 138130
negative_passages.text: If $I$ is a maximal ideal of $R$, why is $R/I$ a field?
negative_passages.docid: 53770
negative_passages.text: Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
negative_passages.docid: 110022
negative_passages.text: Showing prime and maximal ideal
negative_passages.docid: 112150
negative_passages.text: Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
negative_passages.docid: 90314
negative_passages.text: Maximal ideals in $R[x]$