But you really had to be there for the homework. Principle of Virtual Work in the first week of Physics 1. Help!

Oh yeah, another thing about "The Big Red Sleeping Pills": you couldn't remember what you thought you learned the next morning; it went down that easily.

@Michael Renardy: yes, Tim's definition of $f_{1}$ seems like something from computer programming, doesn't it? A conditionally executed function . . .

@Willie Wong: thank you for clarifying this matter.

First of all, thanks to Victor Prostak for providing a negative answer to my to my question. Upon re-thinking it, looking at the structure of $(2, x)$ in $Z[x]$, I remembered the ascending chain condition from a graduate course in abstract algebra I took quite awhile ago, and from several books on ring theory I read in its wake. I soon discovered the wiki page on the Hilbert basis theorem Simon Wadsely mentioned; and yes, that is the kind of thing I was reaching for, though I haven't fully digested it yet. Finally, I assure all it was not homework; I pursued the question on my own.