کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4587532 1334147 2008 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Computing generators of free modules over orders in group algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Computing generators of free modules over orders in group algebras
چکیده انگلیسی

Let E be a number field and G be a finite group. Let A be any OE-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G]≅⊕χMχ is explicitly computable and each Mχ is in fact a matrix ring over a field, this leads to an algorithm that either gives elements α1,…,αd∈X such that X=Aα1⊕⋯⊕Aαd or determines that no such elements exist.Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d=[K:E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be OL, the ring of algebraic integers of L, and A to be the associated order A(E[G];OL)⊆E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K=E=Q.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 320, Issue 2, 15 July 2008, Pages 836-852