Prime \(t\)-ideals in power series rings over a discrete valuation domain
A valuation domain \(V\) is said to be discrete if each primary ideal of \(V\) is a power of its radical. It is known that if \(V\) is a finite-dimensional discrete valuation domain, then \(t\)-dim\(V x=t\)-dim\(V=\text{dim}V\) where \(t\) is the finite character star operation associated to the divisor closure operation \(v\) and \(t\)-dim is the supremum of the lengths of chains of prime \(t\)-ideals (include (0) as a prime \(t\)-ideal). In the paper under review the author shows that if \(V\) is an \(m\)-dimensional discrete valuation domain, then \(t\)-dim\(Vx_1,\dots,x_n=2m-1\) for all \(n\geq2\) and \(t\)-dim\(V[[\{x_{\lambda}\}_{\lambda\in\Lambda}]]_1=2m-1\) for any infinite set \(\{x_{\lambda}\}_{\lambda\in\Lambda}\) of indeterminates over \(V\).
scientific article; zbMATH DE number 5860496