TITLE: Which properties does the polynomial ring $\mathcal{R}[X]$ inherit from the ring $\mathcal{R}$?
QUESTION [6 upvotes]: I've learned that

$\mathcal{R}$ is commutative → $\mathcal{R}[X]$ is commutative
$\mathcal{R}$ has no zero divisors → $\mathcal{R}[X]$ has no zero divisors
$\mathcal{R}$ is unital → $\mathcal{R}[X]$ is unital
$\mathcal{R}$ is factorial → $\mathcal{R}[X]$ is factorial
$\mathcal{R}$ is Noetherian → $\mathcal{R}[X]$ is Noetherian

Which other properties of a polynomial ring are inherited from its coefficient ring? 

List of properties from the comments and answers below (without credits):

$\mathcal{R}$ is reduced → $\mathcal{R}[X]$ is reduced
$\mathcal{R}$ is Abelian → $\mathcal{R}[X]$ is Abelian
$\mathcal{R}$ is nonsingular → $\mathcal{R}[X]$ is nonsingular
$\mathcal{R}$ is 2-primal → $\mathcal{R}[X]$ is 2-primal
$\mathcal{R}$ is Armendariz → $\mathcal{R}[X]$ is Armendariz
$\mathcal{R}$ has characteristic $n$ → $\mathcal{R}[X]$ has characteristic $n$
$\mathcal{R}$ has finite Krull dimension → $\mathcal{R}[X]$ has finite Krull dimension
$\mathcal{R}$ has finite global homological dimension → $\mathcal{R}[X]$ has finite global homological dimension

REPLY [2 votes]: The current contents of DaRT yielded this list:
Properties passing to a polynomial ring of one variable:
nonsingular ring, 2-primal ring, reduced, Armendariz, Abelian, right Noetherian.
Properties not passing to the polynomial ring of one variable:
semicommutative, right principally injective, quasi Frobenius, right coherent, Boolean, periodic, Goldman domain, right Artinian, right principal ideal domain/ring, right self-injective, simple, von Neumann regular, right primitive, semisimple.
This is far from complete, of course, but I'm adding to it as I go.
I think I'm probably missing several of the nice commutative algebraic-geometry flavor rings from the first list, but I won't guess without confirmation.