show the ring is an integral domain
45979
Deﬁne a new addition ⊕ and multiplication on Z by a⊕b = a + b−1 and ab = a + b−ab.
17859
Showing $F[x,y]/(ax^2+by^2-1)$ is a Dedekind domain
141410
Injective integral domains are fields
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
122415
How to show every field is a Euclidean Domain.
80679
Principal ideal rings that are not integral domains
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
4507
Localization of a ring which is not a domain
74139
Subrings of integral domains have the same identity element.
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
74370
$P$ is a prime ideal of $R$ iff $R/P$ is an integral domain. : $P≠R$
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
87078
Prove the following set is an ideal of the ring $Z[x]$
108896
Prime ideal in a polynomial ring over an integrally closed domain
69649
If an ideal contains the multiplicative identity, then it is the whole ring
32839
Example of integral domain with infinitely ascending chain of ideals.
11259
Prove $R\times S$ is not an integral domain