Polynomial ring is not PID
34754
Why is the polynomial ring of more than one variable not a PID?
128213
What's the projective limit of these polynomial rings ?
31451
Proving a subring of $\mathbb{Q}$ containing $\mathbb{Z}$ is a PID
75558
Counter-example for prime ideals in a non commutative ring.
157266
Can a nonzero polynomial evaluate to the zero function in a suitable infinite ring of char 0?
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
58927
Integer coefficient polynomial $p(x)$ has no integer roots of $\,p(0)$ and $p(1)$ are odd [Parity Root Test]
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
132365
Why is absolute value function not a polynomial?
111679
Example of a ring without unity that has a subring with unity?
54875
How to prove polynomials with degree $n$ does not form a vector space?
104789
How to tell an ideal of integer polynomial ring is principal?
40014
A polynomial that is zero on an open set
80679
Principal ideal rings that are not integral domains
35222
Characterizing units in polynomial rings
119297
Finding invertible polynomials in polynomial ring $\mathbb{Z}_{n}[x]$
3037
Integral domain without unity has prime characteristic?