Die Klassengruppe einer kommutativen Ordnung

Halter‐Koch, Franz

doi:10.1002/mana.19941680107

Cited by 1 publication

(4 citation statements)

References 3 publications

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Order By: Relevance

“…, p s } is exactly the set of minimal prime ideals. Hence A is also an order in the sense of [14,Section 3]. Finally, note that A = T (A) = T (Ã).…”

Section: Class Groups and Picard Groupsmentioning

confidence: 96%

“…In this section, we recall and slightly adapt the main results of [14]. Although our primary interest is the computation of Picard groups of O K -orders A ⊆ K [G], where K is a number field and G a finite abelian group, we will work here in greater generality.…”

Section: Class Groups and Picard Groupsmentioning

confidence: 99%

“…This is essentially a reformulation of [14,Satz 10]; see also [18,Satz (12.9) and (12.11)], which covers the case when A is an order in a number field.…”

Section: Class Groups and Picard Groupsmentioning

confidence: 99%

“…In Section 2, we review the basic theoretical results used in our constructions. Our main reference here is [14]. Section 3 forms the heart of the paper, and contains a detailed description of the algorithms for computing the Picard group Pic(A) and the solution of the corresponding refined discrete logarithm problem.…”

Section: Introductionmentioning

confidence: 99%

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Picard Groups and Refined Discrete Logarithms

Bley¹,

Endres²

2005

LMS J. Comput. Math.

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Let K denote a number field, and G a finite abelian group. The ring of algebraic integers in K is denoted in this paper by O K , and A denotes any O K -order in K [G]. The paper describes an algorithm that explicitly computes the Picard group Pic(A), and solves the corresponding (refined) discrete logarithm problem. A tamely ramified extension L/K of prime degree l of an imaginary quadratic number field K is used as an example; the class of O L in Pic(O K [G]) can be numerically determined.

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“…, p s } is exactly the set of minimal prime ideals. Hence A is also an order in the sense of [14,Section 3]. Finally, note that A = T (A) = T (Ã).…”

Section: Class Groups and Picard Groupsmentioning

confidence: 96%

Section: Class Groups and Picard Groupsmentioning

confidence: 99%

“…This is essentially a reformulation of [14,Satz 10]; see also [18,Satz (12.9) and (12.11)], which covers the case when A is an order in a number field.…”

Section: Class Groups and Picard Groupsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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