Prove that $(x-a,y-b)$ is a maximal ideal of $K[x,y]$ (without algebraic geometry)
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
129371
Maximal ideals in the ring of real functions on $[0,1]$
45962
Show that any prime ideal from such a ring is maximal.
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
107463
Is an ideal which is maximal with respect to the property that it consists of zero divisors necessarily prime?
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
116000
Prove that prime ideals of a finite ring are maximal
133975
Localising a polynomial ring and non-maximal prime ideal
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
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.
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 $A$.
45684
Is quotient of a ring by a power of a maximal ideal local?
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
93641
A maximal ideal among those avoiding a multiplicative set is prime
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
587
Ideal Generated by the Union of Two Ideals