Let S be a unital ring, S[t; σ, δ] a skew polynomial ring where σ is an injective endomorphism and δ a left σ-derivation, and suppose f ∈ S[t; σ, δ] 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; σ, δ] 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, σ, δ)-codes over unital rings and to study their behaviour.2010 Mathematics Subject Classification. Primary: 17A60; Secondary: 94B05.
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