Talk:Smooth scheme

The definition of a "regular ring" requires only that it be Noetherian and all of its localizations are regular local: there is no requirement that it be an algebra over a field (or even over any ring). Is it necessary to define "smooth scheme over a field k," rather than just "smooth scheme?" 71.227.119.236 (talk) 11:55, 23 January 2013 (UTC)