Classical and Involutive Invariants of Krull Domains : Springer : 9780792357193 : 0792357191 : 31 Jul 1999 : Just suppose, for a moment, that all rings of integers in algebraic number fields were unique factorization domains, then it would be fairly easy to produce a proof of Fermat's Last Theorem, fitting, say, in the margin of this page. Unfortunately however, rings of integers are not that nice in general, so that, for centuries, math­ ematicians had to search for alternative proofs, a quest which culminated finally in Wiles' marvelous results - but this is history. The fact remains that modern algebraic number theory really started off with in­ vestigating the problem which rings of integers actually are unique factorization domains. The best approach to this question is, of course, through the general the­ ory of Dedekind rings, using the full power of their class group, whose vanishing is, by its very definition, equivalent to the unique factorization property. Using the fact tha