Prime \(t\)-ideals in power series rings over a discrete valuation domain
type: Item
instance of: scholarly article
title: Prime \(t\)-ideals in power series rings over a discrete valuation domain
zbMATH Open document ID: 1209.13012
author: Mi Hee Park
published in: Journal of Algebra
publication date: 2011-03-04T00:00:00Z
review text: 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 \(V\).
reviewed by: Parviz Sahandi
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13F25
Mathematics Subject Classification ID: 13F30
zbMATH DE Number: 5860496
zbMATH Keywords: power series ring
zbMATH Keywords: discrete valuation domain
zbMATH Keywords: prime \(t\)-ideal
zbMATH Keywords: \(t\)-dimension
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.09.015
OpenAlex ID: W2094850892
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DOI: 10.1016/J.JALGEBRA.2010.09.015
description: scientific article; zbMATH DE number 5860496