Definition
Suppose that R is a ring, σ:R → R is an injective ring homomorphism, and δ:R → R is a σ-derivation of R, which means that δ is a homomorphism of abelian groups satisfying
Then the Ore extension R is the ring obtained by giving the ring of polynomials R a new multiplication, subject to the identity
If δ = 0 (i.e., is the zero map) then the Ore extension is denoted R and is called a skew polynomial ring. If σ = 1 (i.e., the identity map) then the Ore extension is denoted R and is called a differential polynomial ring.
Read more about this topic: Ore Extension
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