Why does one define the polynomial ring $R[x] := R^{(\mathbb N)}$ and not as a subset of functions?
104115
Why are polynomials defined to be "formal" (vs. functions)?
147667
Polynomial ring isomorphisms
99835
Polynomial in $\mathbb{Q}[x]$ with root $\sqrt[3]{2}+\sqrt[3]{3}$
155991
Is it the case that every quotient ring ${F[x]}/{(p(x))}$ is a PID?
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
118532
Nilradical of polynomial ring
132365
Why is absolute value function not a polynomial?
34754
Why is the polynomial ring of more than one variable not a PID?
85961
Is the ring and semi-ring definition of algebra and set linked?
137669
$P$ is a monic polynomial of degree $n$ , then which are correct?
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
155604
Show that $k[x,y]/(xy-1)$ is not isomorphic to a polynomial ring in one variable.
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
104789
How to tell an ideal of integer polynomial ring is principal?
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
85633
Rings of polynomials whose (partial) derivatives vanish are Noetherian?
56068
What actually is a polynomial?