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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 leadingcoefficient. Using right division by $f$ to define the multiplication, weobtain 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 thesealgebras. When $S$ is a Galois ring and $f$ base irreducible, these algebrasyield families of finite unital nonassociative rings $A$, whose set of (left orright) 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 overunital rings and to study their behaviour.

Finite nonassociative algebras obtained from skew polynomials and possible applications to $(f,\sigma,\delta)$-codes