کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5772826 1413388 2017 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Indices of Kummer extensions of prime degree
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Indices of Kummer extensions of prime degree
چکیده انگلیسی
Let p be a prime and let ζp be a primitive p-th root of unity. For a finite extension k of Q containing ζp, we consider a Kummer extension L/k of degree p. In this paper, we show that if k=Q(ζp) and the class number of k is one, the index of L/k is one. We also show that if L/k is tamely ramified with a normal integral basis, the index is at most a power of p. In the last section, we show that there exist infinitely many cubic Kummer extensions of Q(ζ3) for both wildly and tamely ramified cases, whose integer rings do not have a power integral basis over that of Q(ζ3).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 11, November 2017, Pages 2815-2826
نویسندگان
, , ,