Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Abstract Algebra: Theory and Applications · Problem 18.4.9
Lattices and Boolean Algebras — Thomas Judson
Mathematics — Abstract Algebra · field-of-fractions-gaussian-integers
Problem Prove that the field of fractions of the Gaussian integers, Z [ i ] \mathbb{Z}[i] Z [ i ] Q ( i ) = { p + q i : p , q ∈ Q } . \mathbb{Q}(i) = \{p + qi : p, q \in \mathbb{Q}\}. Q ( i ) = { p + q i : p , q ∈ Q } . z = a + b i z = a + bi z = a + bi w = c + d i ≠ 0 w = c + di \neq 0 w = c + d i = 0 Z [ i ] \mathbb{Z}[i] Z [ i ] z / w ∈ Q ( i ) z/w \in \mathbb{Q}(i) z / w ∈ Q ( i ) Browse the problem library