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S-unit
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, in the field of algebraic number theory, an S-unit generalises the idea of unit of the ring of integers of the field. Many of the results which hold for units are also valid for S-units. Let K be a number field with ring of integers R. Let S be a finite set of prime ideals of R. An element x of K is an S-unit if the principal fractional ideal (x) is a product of primes in S (to positive or negative powers). For the ring of rational integers Z one may take S to be a finite set of prime numbers and define an S-unit to be a rational number whose numerator and denominator are divisible only by the primes in S. The S-units form a multiplicative group containing the units of R. Dirichlet''s unit theorem holds for S-units: the group of S-units is finitely generated, with rank (maximal number of multiplicatively independent elements) equal to r + s, where r is the rank of the unit group and s = S .
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131205637
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Größe H220mm x B220mm
- EAN 9786131205637
- Format Fachbuch
- Titel S-unit
- Herausgeber Betascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
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