CiteExport$(function(){PrimeFaces.cw("TieredMenu","widget_formSmash_upper_j_idt166",{id:"formSmash:upper:j_idt166",widgetVar:"widget_formSmash_upper_j_idt166",autoDisplay:true,overlay:true,my:"left top",at:"left bottom",trigger:"formSmash:upper:exportLink",triggerEvent:"click"});}); $(function(){PrimeFaces.cw("OverlayPanel","widget_formSmash_upper_j_idt167_j_idt169",{id:"formSmash:upper:j_idt167:j_idt169",widgetVar:"widget_formSmash_upper_j_idt167_j_idt169",target:"formSmash:upper:j_idt167:permLink",showEffect:"blind",hideEffect:"fade",my:"right top",at:"right bottom",showCloseIcon:true});});

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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(English)Manuscript (preprint) (Other academic)
##### Abstract [en]

##### Keywords [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
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt507",{id:"formSmash:j_idt507",widgetVar:"widget_formSmash_j_idt507",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt519",{id:"formSmash:j_idt519",widgetVar:"widget_formSmash_j_idt519",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt530",{id:"formSmash:j_idt530",widgetVar:"widget_formSmash_j_idt530",multiple:true}); 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_idt827:0:j_idt831",widgetVar:"overlay1197311",target:"formSmash:j_idt827:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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