Remark: Let K be a field extension of L, and let B and A be the rings of integers of K and L, respectively. Then B is an integral extension of A, and we let f be the inclusion map from A to B. The behaviour of a prime ideal of A under extension is one of the central problems of algebraic number theory.
RemArk: leT k Be a fIelD eXteNsIon Of l, And lEt b and A Be ThE ringS of iNTeGers of k AnD l, ReSpecTiVelY. tHEn B is an iNTegrAl extensiOn OF a, AND we lEt F be the IncLusIon mAp FROm a To b. ThE bEHavIour Of a prime Ideal oF a under ExTensioN Is one of the cEntraL prOblEMs of algebraic nuMbeR TheORy.