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The Theory of Classical Valuations (Hardcover, 1999 ed.)
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The Theory of Classical Valuations (Hardcover, 1999 ed.)
Series: Springer Monographs in Mathematics
Expected to ship within 10 - 15 working days
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In his studies of cyclotomic fields, in view of establishing his
monumental theorem about Fermat's last theorem, Kummer introduced
"local" methods. They are concerned with divisibility of "ideal
numbers" of cyclotomic fields by lambda = 1 - psi where psi is a
primitive "p"-th root of 1 (p any odd prime). Henssel developed
Kummer's ideas, constructed the field of "p"-adic numbers and
proved the fundamental theorem known today. 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 and
collectively, these topics form the primary focus of this book.
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