Which properties does the polynomial ring $\mathcal{R}[X]$ inherit from the ring $\mathcal{R}$?

Question

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?

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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

Answer 1

A few examples:

"has finite Krull dimension"

"has finite global homological dimension"

"has characteristic $n$", for any $n$

Answer 2

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.