@JulianKuelshammer I don't see what's wrong with #171257...
As a matter of fact, I answered it just now.
Negatively scored questions are not listed under Unanswered tab. The easiest way to deal with unanswerably vague, old questions that the OP failed to improve is to downvote them.
@EinsteinsGrandson Please ask in the main chatroom instead. This is a chatroom with a designated purpose (of answering unanswered questions on the main site).
@brunoh If you click the "share" button of the question, you get a link; the penultimate number of that link is the number of the question. You can then post it like [#number](link) here, and it will turn into what you seek :).
@brunoh I'd love to upvote but since I don't know if your answer is actually correct (nor have the knowledge to obtain such information on short notice), I won't.
@brunoh @Julian Can you check out the message I replied to?
@JackSchmidt I think I have made my answer better, thanks to your help ! (and I forgot the hypothesis of using an algebraically closed field). Can you be kind enough to check it when you have some free time ?
@brunoh looks good (+1). nullstellensatzen tend to require algebraically closed, so I don't think it is a problem to assume it. probably $K[Z]$ cannot inject even into an algebraic extension of $K$.
@JackSchmidt Yes, I do not think the hypothesis of algebraic closure is a bother, since the point was to find an example of strict inequalities, and in this book the author always work in such field. It also saves time here !
@JackSchmidt And thank you for the upvote ! At last (nobody cares during three months. The question was probably just homework) ! This chatroom is useful !
@JackSchmidt I have posted a comment to the answer to the question you kindly checked that shows how to get rid of the hypothesis that the base field is algebraically closed. For the sake of principle and in case you still care a bit. In any case many thanks again !