XmlNamespaceManager is your friend:
string xml = "...";
XmlDocument doc = new XmlDocument();
doc.LoadXml(xml);
XmlNamespaceManager nsm = new XmlNamespaceManager(new NameTable());
nsm.AddNamespace("z", "#RowsetSchema");
XmlNode n = doc.DocumentElement
.SelectSingleNode("//@ows_AZPersonnummer", nsm);
Console.WriteLine(n.Value);
You can also use LINQ to XML:
XDocument xd = XDocument.Parse(xml);
XNamespace xns = "#RowsetSchema";
string result1 = xd.Descendants(xns + "row")
.First()
.Attribute("ows_AZPersonnummer")
.Value;
string result2 =
(from el in xd.Descendants(xns + "row")
select el).First().Attribute("ows_AZPersonnummer").Value;