Ideal Arithmetic and Infrastructure in Purely Cubic Function Fields
نویسنده
چکیده
This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We state algorithms for ideal multiplication and, in the case of unit rank one and characteristic at least five, ideal reduction. The paper concludes with an analysis of the infrastructure in the set of reduced fractional principal ideals of a purely cubic function field of unit rank one and characteristic at least five.
منابع مشابه
Ideal Arithmetic and Infrastructure in Purely Cubic Function Fields Ideal Arithmetic and Infrastructure in Purely Cubic Function Fields
This paper investigates the arithmetic of fractional ideals and the infrastructure of the principal ideal class of a purely cubic function eld of unit rank one. We rst describe how irreducible polynomials split into prime ideals in purely cubic function elds of nonzero unit rank. This decomposition behavior is used to compute so-called canonical bases of fractional ideals; such bases are very s...
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