کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6414273 1630462 2016 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Lattices over cyclic groups and Noether settings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Lattices over cyclic groups and Noether settings
چکیده انگلیسی

For each positive integer m, let ωm be a primitive mth root of 1. Given a prime p, let a be an integer which is a primitive root of 1modp. Let Ip,m be the ideal in Z[ωm] generated by p and ωm−a. Let G be a cyclic group of order n such that the flasque class of any maximal projective ideal in ZG contains a maximal ideal U, of index p for some prime p such that n divides p−1, and such that, Ip,n is principal. It is not known whether the number of groups satisfying this property is finite or infinite. We show that if F is a field of characteristic zero containing all nth roots of 1, then for any ZG-lattice M the fixed subfield of F(M) is stably rational over F. If F also contains primitive mth roots of 1 for all natural numbers m, then for any finite G-module T the fixed subfield of the Noether setting of the group G′=T⋊G is stably rational over F.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 452, 15 April 2016, Pages 212-226
نویسندگان
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