When a field contains the th roots of unity and its characteristic does not divide , Kummer theory identifies cyclic extensions of degree dividing with suitable classes in . Cohomologically,
Articles by others on the same topic
Kummer theory, named after the mathematician Ernst Eduard Kummer, is a branch of number theory that deals with the study of the behavior of prime numbers in relation to fields and their extensions, particularly focusing on certain types of algebraic numbers known as "Kummer extensions." Here are the key points related to Kummer theory: 1. **Kummer Extensions**: These are specific extensions of number fields obtained by adjoining roots of elements.