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This monograph is devoted to Krull domains and its invariants. The book shows how a serious study of invariants of Krull domains necessitates input from various fields of mathematics, including rings and module theory, commutative algebra, K-theory, cohomology theory, localization theory and algebraic geometry. About half of the book is dedicated to so-called involutive invariants, such as the involutive Brauer group, and is essentially the first to cover these topics. In a structured and methodical way, the work presents a large quantity of results previously scattered throughout the...

"Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "

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...