Is p(x) reducible over the rings R?
62757
Showing that a ring is a field as well for one of the provided choices.
133975
Localising a polynomial ring and non-maximal prime ideal
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
77620
Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
121301
What are the roots of an irreducible $p\in F[X]$ in the field extension $F[X]/\langle p\rangle$?
109039
Does this "extension property" for polynomial rings satisfy a universal property?
90314
Maximal ideals in $R[x]$
77209
Reducibility of $x^3+nx+1$ over $ \Bbb Z$
10627
When is $X^n-a$ is irreducible over F?
2907
How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
138275
Show $100+t$ is reducible in $\mathbb{Z}[[t]]$
147047
Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
29545
$[(x-a_1)(x-a_2) \cdots (x-a_n)]^2 +1$ is irreducible over $\mathbb Q$
122958
$R/I$ is commutative iff $rs-sr \in I$
140865
Rings' second isomorphism theorem
41398
For a ring $R$, does $\operatorname{End}_R(R)\cong R^{\mathrm{op}}$?