کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4582399 1333798 2014 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Roots of solvable polynomials of prime degree
ترجمه فارسی عنوان
ریشه های چند جملهای قابل حل اول درجه
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

An explicit formula for the most general root of a solvable polynomial of prime degree is stated and proved. Such a root can be expressed rationally in terms of a single compound radical determined by the roots of a cyclic polynomial whose degree divides μ−1μ−1, where μμ is the prime. The study of such formulas was initiated by a formula of Abel for roots of quintic polynomials that are solvable, and was carried forward by Kronecker and a few others, but seems to have lain dormant since 1924. A formula equivalent to the one given here is contained in a paper of Anders Wiman in 1903, but it seems to have been forgotten.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Expositiones Mathematicae - Volume 32, Issue 1, 2014, Pages 79–91
نویسندگان
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