Any finite integral domain is a field
48765
Let $S$ and $T$ be finite non-empty sets such that $|S| = |T|$. Show that the function $f : S\to T$ is onto if and only if it is one-to-one.
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
134773
A domain is a field if it has a common multiple $\!\neq\! 0$ of all elements $\!\neq\! 0$
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
92677
Infinite algebraic extension of a finite field
122415
How to show every field is a Euclidean Domain.
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
23242
Commutative integral domain with d.c.c. is a field
34740
Do finite algebraically closed fields exist?
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
134458
Isomorphisms preserving integral domains and fields
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
138911
Is $\mathbb R^2$ a field?
79725
Fields of arbitrary cardinality
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question