Kurschak formally introduced the concept of a valuation of a field, as being real valued functions on the set of non-zero elements of the field satisfying certain properties, like the p-adic valuations. Ostrowski, Hasse, Schmidt and others developed this theory. These are the topics which are the object of this book.
Area of great interest where there is no book to serve as a first introduction to the topic * Fully up-to-date as the author draws upon his long-standing experience * Ribenboim has written other successful Springer titles * Fills a niche in the literature and will serve as the ultimate resource on the subject
Paulo Ribenboim
Algebra Division Finite Topology commutative property function fundamental theorem theorem
"It is well written, encyclopedic, and authoritative and probably belongs on the shelf of any commutative algebraist or algebraic number theorist."--MATHEMATICAL REVIEWS