Let R be a commutative ring with identity. Prove that R is a field if and only if (0R) is a maximal ideal.
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
30714
A question on ring homomorphisms and maximal ideals.
48537
If $\forall x \in R, x^2-x \in Z(G)$, than $R$ is commutative
36996
If $x^{2}-x\in Z(R)$ for all $x\in R$, then $R$ is commutative.
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
14055
How to show that a finite commutative ring without zero divisors is a field?
85913
R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
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
100961
Ideals in valuation rings
136985
Every finite commutative ring $R$ must be of the form
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$