More generally, if be any Abelian number field whose Galois group over is denoted , then the Stickelberger element of and the Stickelberger ideal of can be defined. By the Kronecker–Weber theorem there is an integer such that is contained in . Fix the least such (this is the (finite part of the) conductor of over ). There is a natural group homomorphism given by restriction, i.e. if , its image in is its restriction to denoted . The Stickelberger element of is then defined as