query: Prove that $I$ is a maximal ideal of $\mathcal A$.
positive_passages.docid: 28244
positive_passages.text: Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
negative_passages.docid: 57198
negative_passages.text: How to show that a valuation ring has a unique maximal ideal?
negative_passages.docid: 87780
negative_passages.text: Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
negative_passages.docid: 43230
negative_passages.text: Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
negative_passages.docid: 96144
negative_passages.text: Every element outside the maximal ideal of a local ring is a unit
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: 80232
negative_passages.text: Suppose that R is a commutative ring with unity such that for each $a$ in $R$ there is an integer $n > 1\mid a^n =a$. Every prime ideal is maximal?
negative_passages.docid: 148208
negative_passages.text: In Noetherian ring $R$, ideal $I\subset R$, $P\in\mathrm{Ass}(I),P=I:a$ for some $a\in R$.
negative_passages.docid: 6699
negative_passages.text: An ideal that is maximal among non-finitely generated ideals is prime.
negative_passages.docid: 45684
negative_passages.text: Is quotient of a ring by a power of a maximal ideal local?
negative_passages.docid: 20877
negative_passages.text: The set of all nilpotent elements is an ideal
negative_passages.docid: 136654
negative_passages.text: $(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
negative_passages.docid: 111996
negative_passages.text: Maximal and Prime Ideal in Z
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: 110022
negative_passages.text: Showing prime and maximal ideal
negative_passages.docid: 84663
negative_passages.text: $A$ local Noetherian ring with principal maximal ideal implies PIR?
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