  Let $S$ be a unital ring, $S[t;\sigma,\delta]$ a skew polynomial ring where
$\sigma$ is an injective endomorphism and $\delta$ a left $\sigma$-derivation,
and suppose $f\in S[t;\sigma,\delta]$ has degree $m$ and an invertible leading
coefficient. Using right division by $f$ to define the multiplication, we
obtain unital nonassociative algebras $S_f$ on the set of skew polynomials in
$S[t;\sigma,\delta]$ of degree less than $m$. We study the structure of these
algebras. When $S$ is a Galois ring and $f$ base irreducible, these algebras
yield families of finite unital nonassociative rings $A$, whose set of (left or
right) zero divisors has the form $pA$ for some prime $p$. For reducible $f$,
the $S_f$ can be employed both to design linear $(f,\sigma,\delta)$-codes over
unital rings and to study their behaviour.
