Standard name for ideals generated by a subset of indeterminates? I have been working on a problem in the polynomial ring $k[x_1,\ldots,x_n]$, where I've been dealing with ideals generated by subsets of the indeterminates, i.e.,
ideals of the form $$\langle x_i\mid i\in A\rangle,$$ for subsets $A\subseteq \{1,\ldots,n\}$.
Is there a standard name for such ideals? 

Well, I had guessed that "coordinate ideal" would be a natural name, but that term didn't come up in a first google search. However, I have just found a paper that does indeed used this term, and so that settles it for me. 
