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Computing the ideal class monoid of an orderPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); (English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### Keyword [en]

ideal classes, orders, number fields, integral matrices
##### National Category

Algebra and Logic
##### Research subject

Mathematics
##### Identifiers

URN: urn:nbn:se:su:diva-155131OAI: oai:DiVA.org:su-155131DiVA, id: diva2:1197210
#####

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#####

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#####

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Available from: 2018-04-12 Created: 2018-04-12 Last updated: 2018-04-12Bibliographically approved
##### In thesis

There are well known algorithms to compute the class group of the maximal order of a number field K and the group of invertible ideal classes of a non-maximal order R. In this paper we explain how to compute also the isomorphism classes of non-invertible ideals of an order R in a finite product of number fields K. In particular we also extend the above-mentioned algorithms to this more general setting. Moreover, we generalize a theorem of Latimer and MacDuffee providing a bijection between the conjugacy classes of integral matrices with given minimal and characteristic polynomials and the isomorphism classes of lattices in certain Q-algebras, which under certain assumptions can be explicitly described in terms of ideal classes.

1. Computing abelian varieties over finite fields$(function(){PrimeFaces.cw("OverlayPanel","overlay1197311",{id:"formSmash:j_idt1574:0:j_idt1581",widgetVar:"overlay1197311",target:"formSmash:j_idt1574:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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