If $R$ is a Boolean ring which is in fact a field, then it must be isomorphic to $\mathbb Z / 2 \mathbb Z$
101164
Show that $B \cong \mathbb Z /2\mathbb Z$ for a Boolean field B
144105
Ring homomorphism from $\mathbb Z$ to $\mathbb Z$ is always identity or $0$
157863
A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
25764
Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)
26749
$\mathbb{Z}[X]/(X^2-1)$ is not isomorphic with $\mathbb{Z}\times \mathbb{Z}$
144245
Shorter proof of $R/I$ is a field if and only if $I$ is maximal
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
39576
Quotient ring being isomorphic to the initial ring
34668
Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$
41846
$(\mathbb{R}^n,\|\cdot\|_{p})$ is isometrically isomorphic to $(\mathbb{R}^n,\|\cdot\|_{q})$ iff $p=q,$
7899
Show that if $p$ is prime then $\Bbb Z_p$ is a field
26661
Ring homomorphisms from $\mathbb{Z}_n$ to $\mathbb{Z}_m$
137011
showing $\psi: R\to \mathbb C$ is ring isomorphism.
1686
Show that quotient rings are not isomorphic
76813
The ring $ℤ/nℤ$ is a field if and only if $n$ is prime
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain