query: Maximal ideal in $\mathfrak{R}[x]$
positive_passages.docid: 77862
positive_passages.text: Question about fields and quotients of polynomial rings
negative_passages.docid: 113582
negative_passages.text: How can I find an element $x\not\in\mathfrak mM_{\mathfrak m}$ for every maximal ideal $\mathfrak m$
negative_passages.docid: 89782
negative_passages.text: To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
negative_passages.docid: 1580
negative_passages.text: An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
negative_passages.docid: 93629
negative_passages.text: Ideal quotient of fractional ideals
negative_passages.docid: 92071
negative_passages.text: A maximal ideal is always a prime ideal?
negative_passages.docid: 124151
negative_passages.text: Finite ring extension and number of maximal ideals
negative_passages.docid: 13901
negative_passages.text: Finitely many prime ideals lying over $\mathfrak{p}$
negative_passages.docid: 109199
negative_passages.text: Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
negative_passages.docid: 19230
negative_passages.text: Prime/Maximal Ideals in $\mathbb{Z}[\sqrt d]$
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: 120181
negative_passages.text: The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
negative_passages.docid: 149412
negative_passages.text: Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
negative_passages.docid: 93658
negative_passages.text: Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
negative_passages.docid: 131497
negative_passages.text: Maximal ideal not containing the set of powers of an element is prime
negative_passages.docid: 129371
negative_passages.text: Maximal ideals in the ring of real functions on $[0,1]$
negative_passages.docid: 46040
negative_passages.text: Preimage of maximal ideal is maximal (why is this answer wrong?)