A generalization of the ring of skew Ore polynomials (Q2710710)

An associative ring \(A\) is called a left ring of skew polynomials over a subring \(K\) if there exists an element \(t\in A\) such that every element \(a\in A\) has a unique representation \(a=\alpha_0+\alpha_1 t+\cdots+\alpha_m t^m\), where \(\alpha_i\in K\) for all \(i\). In particular if \(a\in K\), then \(t^ma=\sum_{i\geq 0}\psi_i^{(m)}(a)t^i\), where \(\psi_i^{(m)}(a)\in K\). The operators \(\psi_i^{(m)}\), \(i\geq 0\), \(m\geq 1\), satisfy some specific relations which also depend on all elements from \(K\). It is shown that this set of relations constitutes a criterion under which a skew polynomial ring \(A\) really exists. This result is strengthened to the case when the specific relations depend only on a set of generators of the ring \(K\).