Is this ring an integral domain? Prove or give a counterexample
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
52966
Rings, ideals and units-proof
85987
Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain
92420
Characteristic of  a Non-unital Integral Ring
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
151794
Can an ideal in a commutative integral domain be its own square?
141659
Every field is an integral domain
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.
126503
Showing that an integral domain is a PID if it satisfies two conditions
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
23242
Commutative integral domain with d.c.c. is a field