Number fields #
This file defines a number field and the ring of integers corresponding to it.
Main definitions #
number_fielddefines a number field as a field which has characteristic zero and is finite dimensional over ℚ.
ring_of_integersdefines the ring of integers (or number ring) corresponding to a number field as the integral closure of ℤ in the number field.
Implementation notes #
The definitions that involve a field of fractions choose a canonical field of fractions, but are independent of that choice.
- D. Marcus, Number Fields
- J.W.S. Cassels, A. Frölich, Algebraic Number Theory
- [P. Samuel, Algebraic Theory of Numbers][samuel1970algebraic]
number field, ring of integers
The ring of integers of
K are equivalent to any integral closure of