On twisted group rings and Galois-stable ideals

dc.contributor.authorKrauß, Nora
dc.date.accessioned2025-01-15T07:54:56Z
dc.date.available2025-01-15T07:54:56Z
dc.date.issued2015de
dc.description.abstractLet 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.other1920497951
dc.identifier.urihttp://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-155268de
dc.identifier.urihttp://elib.uni-stuttgart.de/handle/11682/15526
dc.identifier.urihttps://doi.org/10.18419/opus-15507
dc.language.isoende
dc.rightsinfo:eu-repo/semantics/openAccessde
dc.subject.ddc510de
dc.titleOn twisted group rings and Galois-stable idealsen
dc.typebachelorThesisde
ubs.fakultaetMathematik und Physikde
ubs.institutFakultät Mathematik und Physik (Institutsübergreifend)de
ubs.publikation.seiten76de
ubs.publikation.typAbschlussarbeit (Bachelor)de

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