In algebra, Zariski's lemma, proved by Oscar Zariski (1947), states that, if a field K is finitely generated as an associative algebra over another field k, then K is a finite field extension of k; that is, K is finitely generated as a module (in other words, K is a finite dimensional vector space) over k. An important application of the lemma is a proof of the weak form of Hilbert's Nullstellensatz: if I is a proper ideal of k [ t 1 , .
In algebra, Zariski's lemma, proved by Oscar Zariski (1947), states that, if a field K is finitely generated as an associative algebra over another field k, then K is a finite field extension of k; that is, K is finitely generated as a module (in other words, K is a finite dimensional vector space) over k. An important application of the lemma is a proof of the weak form of Hilbert's Nullstellensatz: if I is a proper ideal of k [ t 1 , .
Source: Wikipedia "Zariski's lemma" · CC BY-SA 4.0
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