Let R be an integral domain. Show that if the only ideals in R are {0} and R itself, R must be a field
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
131943
How to directly prove that $M$ is maximal ideal of $A$ iff $A/M$ is a field?
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
76661
Checking the maximality of a principal ideal in $R[x]$
551
Why is a finite integral domain always field?
23242
Commutative integral domain with d.c.c. is a field
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
134773
A domain is a field if it has a common multiple $\!\neq\! 0$ of all elements $\!\neq\! 0$
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
13174
Show that $A[X]/(aX+b)$ is an integral domain
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain
14055
How to show that a finite commutative ring without zero divisors is a field?
141659
Every field is an integral domain
74139
Subrings of integral domains have the same identity element.