Krauß, Nora2025-01-152025-01-1520151920497951http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-155268http://elib.uni-stuttgart.de/handle/11682/15526https://doi.org/10.18419/opus-15507Let 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.eninfo:eu-repo/semantics/openAccess510bachelorThesis