Talk:Dimension of an algebraic variety
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Field of definition
[edit]the article needs to be edited in one of the following two ways:
1. add the assumption that the field K is algebraically closed. 2. explain that some of the definitions are only equivalent if K is algebraically closed (or what definition of "variety," "algebraic set," etc. is being used).
I prefer approach (1). — Preceding unsigned comment added by 128.179.145.222 (talk) 11:59, 28 January 2014 (UTC)
- The standard definition of "point of an algebraic variety" is "point with coordinates in an algebraically closed field". This is this standard definition that is implicitly used here. I agree that saying it explicitly is better. It would also be better to say that the dimension does not change if the field K is enlarged or its algebraically closed extension is changed. Also a section about the real dimension (the dimension of the set of real points) would be useful. I have implemented all these clarifications. D.Lazard (talk) 13:18, 28 January 2014 (UTC)