Proving $(x_1 - a_1, \ldots, x_n -a_n)$ is a maximal ideal
30327
$\ker \phi = (x_1-a_1, ..., x_n-a_n)$ for a ring homomorphism $\phi: R[x_1, ..., x_n] \to R$
136710
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
99715
Proper ideal and units proof
54916
Maximal ideal in commutative ring
89782
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
43889
Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$
74537
Maximal Ideals in $K[y]$
96144
Every element outside the maximal ideal of a local ring is a unit
1580
An integral domain $A$ is exactly the intersection of the localisations of $A$ at each maximal ideal
80397
Show that this set of polynomials is ideal in F[x]
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
89313
Maximal ideals of polynomial rings in infinitely many variables
63207
Zorn's lemma and maximal ideals