Ostrowski quotients for finite extensions of number fields

Abstract

For a number field L, the Pólya group of L is the subgroup Po(L) of the ideal class group of L generated by all classes of Ostrowski ideals of L [17]. Relativizing this notion, the relative Pólya group Po(L/K), for L/K a finite extension of number fields, has been recently introduced independently in [3,15]. Assuming L/K is Galois, we find some applications of an exact sequence in [15] for the capitulation problem, including a new proof of Hilbert's theorem 94. Then we define the Ostrowski quotient Ost(L/K) and generalize some known results for P o(L) to Ost(L/K).