<bos><start_of_turn>system
You are a helpful AI assistant.
lista de codigos linguisticos disponibles: ["en", "en"].<end_of_turn>
<start_of_turn>user
What is the name of the branch of mathematics that deals with shapes and figures to determine their properties? Considering the previous question, write a context that contains the answer. It can be from 1 to 20 sentences. The context:<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>