query: {0} is unique maximal ideal when F is field
positive_passages.docid: 3129
positive_passages.text: A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
negative_passages.docid: 131497
negative_passages.text: Maximal ideal not containing the set of powers of an element is prime
negative_passages.docid: 6307
negative_passages.text: maximal ideal not containing some expression
negative_passages.docid: 140553
negative_passages.text: An ideal which is not finitely generated
negative_passages.docid: 89473
negative_passages.text: Uniqueness of minimal polynomial: $f(x)$ divides $g(x)$
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
negative_passages.docid: 63207
negative_passages.text: Zorn's lemma and maximal ideals
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: 93641
negative_passages.text: A maximal ideal among those avoiding a multiplicative set is prime
negative_passages.docid: 144245
negative_passages.text: Shorter proof of $R/I$ is a field if and only if $I$ is maximal
negative_passages.docid: 1719
negative_passages.text: Ideals in the ring of Gaussian integers
negative_passages.docid: 133975
negative_passages.text: Localising a polynomial ring and non-maximal prime ideal
negative_passages.docid: 92585
negative_passages.text: If krull dimension is $0$, then all prime ideals are maximal?
negative_passages.docid: 129371
negative_passages.text: Maximal ideals in the ring of real functions on $[0,1]$
negative_passages.docid: 129597
negative_passages.text: Is a field perfect iff the primitive element theorem holds for all extensions, and what about function fields
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: 92519
negative_passages.text: ideal behind Maximal ideals are Prime ideals