The construction of solvable polynomials
نویسندگان
چکیده
منابع مشابه
The Construction of Solvable Polynomials
Although Leopold Kronecker’s 1853 paper “On equations that are algebraically solvable” is famous for containing his enunciation of the Kronecker-Weber theorem, its main theorem is an altogether different one, a theorem that reduces the problem of constructing solvable polynomials of prime degree μ to the problem of constructing cyclic polynomials of degree μ− 1. Kronecker’s statement of the the...
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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 − 1, where μ is the prime. The study of such formulas was initiated by a formula of Abel for roots of quintic polynomials that are solvable,...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2009
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-09-01253-1