Show that an integral domain with finitely many ideals is a field
23242
Commutative integral domain with d.c.c. is a field
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
74139
Subrings of integral domains have the same identity element.
132193
Why $\Bbb Z$ = (integers) is an integral domain?
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
116000
Prove that prime ideals of a finite ring are maximal
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?
141410
Injective integral domains are fields
31049
If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
151794
Can an ideal in a commutative integral domain be its own square?
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
16643
A slick proof that a field which is finitely generated as a ring is finite
119699
Examples of Cohen-Macaulay integral domains
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
8317
Understanding a proof of "If $R$ is an integral domain, then $R[x]$ is an integral domain as well".
32839
Example of integral domain with infinitely ascending chain of ideals.