In algebraic number theory, a reflection theorem or Spiegelungssatz (German for reflection theorem – see Spiegel and Satz) is one of a collection of theorems linking the sizes of different ideal class groups (or ray class groups), or the sizes of different isotypic components of a class group. The original example is due to Ernst Eduard Kummer, who showed that the class number of the cyclotomic field, with p a prime number, will be divisible by p if the class number of the maximal real subfield is. Another example is due to Scholz. A simplified version of his theorem states that if 3 divides the class number of a real quadratic field, then 3 also divides the class number of the imaginary quadratic field .
Read more about Reflection Theorem: Leopoldt's Spiegelungssatz, Extensions
Famous quotes containing the words reflection and/or theorem:
“A little reflection will enable any person to detect in himself that setness in trifles which is the result of the unwatched instinct of self-will and to establish over himself a jealous guardianship.”
—Harriet Beecher Stowe (1811–1896)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)