query: Prove that $\langle x-a, y-b, z-c\rangle$ is a maximal ideal in $K[x,y,z]$
positive_passages.docid: 464
positive_passages.text: Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 133706
negative_passages.text: If R is a local ring, then its maximal left-ideal is a left and right ideal
negative_passages.docid: 109199
negative_passages.text: Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
negative_passages.docid: 98352
negative_passages.text: If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
negative_passages.docid: 116430
negative_passages.text: If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
negative_passages.docid: 116943
negative_passages.text: Proof for maximal ideals in $\mathbb{Z}[x]$
negative_passages.docid: 20877
negative_passages.text: The set of all nilpotent elements is an ideal
negative_passages.docid: 102341
negative_passages.text: Primary decomposition of a monomial ideal
negative_passages.docid: 146714
negative_passages.text: Rees algebra of a monomial ideal
negative_passages.docid: 44083
negative_passages.text: prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
negative_passages.docid: 155745
negative_passages.text: Ideals of $\mathbb{Z}[X]$
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 120181
negative_passages.text: The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
negative_passages.docid: 30714
negative_passages.text: A question on ring homomorphisms and maximal ideals.
negative_passages.docid: 99715
negative_passages.text: Proper ideal and units proof
negative_passages.docid: 587
negative_passages.text: Ideal Generated by the Union of Two Ideals