symmetric monoidal (∞,1)-category of spectra
An Ore extension of a unital ring $R$ is certain generalization of the ring $R[T]$ of polynomials in one variable $T$ with coefficients in $R$.
While keeping the left $R$-module-structure intact, unlike in the polynomial ring, the coefficients in $R$ and the indeterminate $T$ do not need to commute, but rather commute up to a skew-derivation. A skew-polynomial ring is a special case.
Given an endomorphism $\sigma: R\to R$, a $\sigma$-derivation $d: R\to R$ is an additive map satisfying the $\sigma$-twisted Leibniz rule
If $\sigma$ is an injective endomorphism of $R$, and $d$ a $\sigma$-derivation $d$ then the free left $R$-module underlying the ring of polynomials in one variable $R[T]$ is equipped with the unique multiplication rule which is making it into a unital ring, extends $R = R 1\subset R[T]$ and such that
$R[T]$ with this ring structure is called the Ore extension of $R$ and denoted $R[T;\sigma,d]$. If $d = 0$ identically, then we say that $R[T]$ is a skew polynomial ring.
An Ore extension of an Ore extension of…(finitely many times) is called an iterated Ore extension. See quantum nilpotent algebra for an example.
Last revised on July 1, 2024 at 20:45:32. See the history of this page for a list of all contributions to it.