On twisted group rings and Galois-stable ideals
dc.contributor.author | Krauß, Nora | |
dc.date.accessioned | 2025-01-15T07:54:56Z | |
dc.date.available | 2025-01-15T07:54:56Z | |
dc.date.issued | 2015 | de |
dc.description.abstract | Let A be a Dedekind domain with perfect field of fractions K, and let B be the integral closure of A in a finite Galois extension L of K, with Galois group G := Gal(L|K). We describe the twisted group ring B~G by means of a Wedderburn-embedding. We give a description of the image of B~G in A^(n×n) via congruences of matrix entries for an extension of the form Q(√d)|Q with d being a nonzero squarefree integer, in case of a cyclotomic field Q(ζ_p)|Q with p ∈ Z_>0 prime, and for the extensions Q(ζ_9)|Q and Q(2^{1/3}, ζ_3)|Q. By means of this description we show in examples that there are non-zero ideals in B~G that are not of the form b(B~G) for some Galois-stable ideal b ⊆ B. In case of A being a finite extension of Z, we obtain an explicit formula for the index of the image of B~G in A^(n×n) in terms of the discriminant. | en |
dc.identifier.other | 1920497951 | |
dc.identifier.uri | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-155268 | de |
dc.identifier.uri | http://elib.uni-stuttgart.de/handle/11682/15526 | |
dc.identifier.uri | https://doi.org/10.18419/opus-15507 | |
dc.language.iso | en | de |
dc.rights | info:eu-repo/semantics/openAccess | de |
dc.subject.ddc | 510 | de |
dc.title | On twisted group rings and Galois-stable ideals | en |
dc.type | bachelorThesis | de |
ubs.fakultaet | Mathematik und Physik | de |
ubs.institut | Fakultät Mathematik und Physik (Institutsübergreifend) | de |
ubs.publikation.seiten | 76 | de |
ubs.publikation.typ | Abschlussarbeit (Bachelor) | de |