If $R$ has zero divisors, does $R[x]$ have invertible polynomials of degree greater than $0$?
35222
Characterizing units in polynomial rings
116856
Proving that a polynomial of the form $(x-a_1)\cdots(x-a_n) + 1$ is irreducible over $\mathbb{Q}$
155962
Are there irreducible polynomials that are partially solvable by radicals?
70249
Irreducibility of Polynomials in $k[x,y]$
33052
How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime
18066
Prove that any non-zero-divisor of a finite dimensional algebra has an inverse
29452
Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
20790
What are irreducibles in the ring $R$ of entire functions?
139017
If a polynomial takes integer values at every integer, does it have integer coefficients?
27577
An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
125604
Proof that $\mathbb{Z}$ has no zero divisors
148813
Prove: $f: \mathbb{R} \rightarrow \mathbb{R}$ st for every $x \in \mathbb{R}$ there exists $n$ st $f^{(n)}(x) = 0$, f is a polynomial.
134442
Can a matrix in $\mathbb{R}$ have a minimal polynomial that has coefficients in $\mathbb{C}$?
100340
Invariant dimension property on a ring without zero divisors
100862
Polynomials with rational zeros
77820
Roots in a polynomial ring
68807
How to show that the ring $S/A$ has no zero divisors? (Hungerford, Algebra, Problem 12, Chapter III, Section 2)