Foundations of the Theory of Algebraic Numbers, Volume 1"The exploitation of these two great theories (Dedekind, with the theory of moduls and ideals; Kronecker with the methodical use of the theory of forms with indetermiante coefficients and of the modular systems) is the main object of this book." - p. vi. |
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a₁ algebraic integers algebraic modul algebraic numbers algebraic quantity algebraic realm algebraic unit arbitrary number b₁ basal elements c₁ coefficients belong complete system congruence consequently Dedekind definition denote determinant different from zero discriminant equal evident expressed fi(x finite modul finite number fixed realm form a basis formula function F(x further greatest common divisor Hence highest power integral coefficients integral function integral values irreducible equation Kronecker least common multiple linear form linearly independent modd norm normal divisors normal realm nth degree nth order number divisible Pell's equation preceding article prime function prime ideal prime integer primitive quantity proved quantities a1 rational function rational integers rational numbers realm of rationality realm R(x relatively prime ring ideal roots satisfies an irreducible satisfies the irreducible seen stock-realm Suppose system of residues unity variables w₂ write x₁ απ