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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
5
votes
Tweetable Mathematics
There is a way of pretending that any reduced ring is Noetherian and a field. Grothendieck's generic freeness lemma is then quite easy. link (Section 11.5)
10
votes
Alternate proofs of Hilberts Basis Theorem
Sorry, this is not an answer, but rather a too-long elaboration on constructive aspects. I post this here because there was some interest about the constructive content of the theorem in the comments. …