Everything about Algebraic Number Theory totally explained
Algebraic number theory is a branch of
number theory in which the concept of a
number is expanded to the
algebraic numbers, which are
roots of
polynomials with
rational coefficients. An
algebraic number field is any finite (and therefore
algebraic)
field extension of the rational numbers. These fields contain elements analogous to the
integers, the so-called
algebraic integers. In this setting, the familiar features of the integers (for example,
unique factorization) need not hold. The virtue of the machinery employed —
Galois theory,
group cohomology,
class field theory,
group representations and
L-functions — is that it allows one to recoverthat order partly for this new class of numbers.
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