<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["de", "en"].<end_of_turn>
<start_of_turn>user
Wie heißt der Zweig der Mathematik, der sich mit Formen und Figuren beschäftigt, um deren Eigenschaften zu bestimmen? Schreiben Sie unter Berücksichtigung der vorherigen Frage einen Kontext, der die Antwort enthält. Es kann zwischen 1 und 20 Sätzen lang sein. Der Kontext:<end_of_turn>
<start_of_turn>model
In ring theory, the notion of number is generally replaced by that of ideal. Prime ideals, which generalize prime elements in the sense that the prime ideal generated by a prime element is a prime ideal, are an important tool and object of study in commutative algebra, algebraic number theory, and algebraic geometry. The prime ideals of the ring of integers are the ideals (0), (2), (3), (5), (7), (11),... The fundamental theorem of arithmetic generalizes to Lasker's theorem. Noether, which expresses each ideal in a Noetherian commutative ring as an intersection of prime ideals, which are the appropriate generalizations of prime powers.<end_of_turn><eos>