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| S-unit equation ： ウィキペディア英語版 |
S-unit
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.
==Definition==
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''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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