Ramification of ideals through ring/algebra homomorphisms is the dual incarnation of branch points of branched covering spaces.
Given a ring injection (for instance the inclusion of in , where is a field extension and (resp. ) is the ring of integers of (resp. )), then a prime ideal is said to be ramified in if is not a prime ideal anymore.
Here will be a product of powers of prime ideals of , and the ramification index of at a prime ideal of is the power with which this appears.
Kummer's theorem?
Last revised on March 1, 2021 at 05:35:28. See the history of this page for a list of all contributions to it.