compositum

plural compositums

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

   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.

   2 more examples

   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).

   2004, Dinesh S. Thakur, Function Field Arithmetic, World Scientific, page 81

   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.

   2005, T. Y. Lam, Introduction to Quadratic Forms over Fields, American Mathematical Society, page 333

   Synonyms: field compositum