query: Prove that if $R/I$ is a field then $I$ is maximal
positive_passages.docid: 144245
positive_passages.text: Shorter proof of $R/I$ is a field if and only if $I$ is maximal
negative_passages.docid: 138572
negative_passages.text: Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
negative_passages.docid: 54916
negative_passages.text: Maximal ideal in commutative ring
negative_passages.docid: 44083
negative_passages.text: prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
negative_passages.docid: 13983
negative_passages.text: Show that If $R[X]$ is Euclidean domain then $R$ is a field
negative_passages.docid: 74663
negative_passages.text: Is $\mathbb{R}$ an algebraic extension of some proper subfield?
negative_passages.docid: 104377
negative_passages.text: Maximal Ideals in Ring of Continuous Functions
negative_passages.docid: 129371
negative_passages.text: Maximal ideals in the ring of real functions on $[0,1]$
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: 58424
negative_passages.text: If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
negative_passages.docid: 16643
negative_passages.text: A slick proof that a field which is finitely generated as a ring is finite
negative_passages.docid: 122958
negative_passages.text: $R/I$ is commutative iff $rs-sr \in I$
negative_passages.docid: 63207
negative_passages.text: Zorn's lemma and maximal ideals
negative_passages.docid: 130466
negative_passages.text: Proving every prime ideal is maximal in a finite dimensional ring over a field.
negative_passages.docid: 93723
negative_passages.text: Find all the maximal ideals in the ring $\mathbb{R}[x]$.
negative_passages.docid: 110022
negative_passages.text: Showing prime and maximal ideal
negative_passages.docid: 80961
negative_passages.text: Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain