Meaning of compositum | Babel Free

Definitions

Given a field extension F/K and subextensions A and B, the smallest subextension that contains both A and B.

Examples

“1998, Iain T. Adamson (translator), David Hilbert, The Theory of Algebraic Number Fields, [1897, D. Hilbert, Zahlbericht], Springer, page 98, Of particular interest is the case in which the discriminants of the fields forming the compositum are relatively prime.”

“For #92;Q, we get the maximal abelian extension by adjoining all roots of unity, i.e., taking compositum of all m-th cyclotomic fields (this is the famous Kronecker-Weber theorem).”

“This is then just the field compositum of all the quadratic extensions F(#92;sqrt#123;a#95;i#125;) in the algebraic closure of F.”

CEFR level