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• W2255958584 endingPage "634" @default.
• W2255958584 startingPage "615" @default.
• W2255958584 abstract "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 $fin S[t;sigma,delta]$ 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." @default.
• W2255958584 created "2016-06-24" @default.
• W2255958584 creator A5063477722 @default.
• W2255958584 date "2017-01-01" @default.
• W2255958584 modified "2023-09-26" @default.
• W2255958584 title "Finite nonassociative algebras obtained from skew polynomials and possible applications to (<i>f</i>, <i>σ</i>, <i>δ</i>)-codes" @default.
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• W2255958584 doi "https://doi.org/10.3934/amc.2017046" @default.
• W2255958584 hasPublicationYear "2017" @default.
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