Extending valuation rings to \(K(x,\sigma)\) (Q2785924)

Let \(R_0\) be a subring of a skew field \(K_0\) such that \(a\in K_0\setminus R_0\) implies \(a^{-1}\in R_0\); then \((K_0,R_0)\) is called a valued skew field. Some results about the extensions of valued skew field \((K_0,R_0)\) in \(K_1\) are proved, where \(K_1=K_0(x,\sigma)\) is an Ore extension of \(K_0\) and \(\sigma\) is a monomorphism of \(K_0\), or \(K_1=Q(K_0G)\) is the skew field of quotients of the group ring \(K_0G\), where \(G\) is a right ordered group such that \(K_0G\) is an Ore domain. Constructive methods for examples are also given where \(R_0\) has no extension in \(K_1\) and also where families of extensions with certain properties exist.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].