algebraic number field in a sentence
1) Another notion needed to define algebraic number fields is vector spaces.
algebraic collocations
2) Algebraic number theory studies algebraic number fields .
3) A related class of fields very important in number theory are algebraic number fields .
algebraic number field example sentences
4) The notion of algebraic number field relies on the concept of a field.5) Landau prime ideal theorem for a generalization to prime ideals in algebraic number fields .
6) Algebraic number fields and function fields over F"q" are further global fields.
7) Finite extensions of Q are also called algebraic number fields and are important in number theory.
8) Let __FORMULA__ be a "Galois extension" of algebraic number fields with automorphism group __FORMULA__.
9) Obvious examples are the rings of integers of algebraic number fields as well as the rational numbers.
10) fields of algebraic numbers are also called " algebraic number fields ", or shortly "number fields".
11) The extended Riemann hypothesis extends the Riemann hypothesis to all Dedekind zeta functions of algebraic number fields .
12) There has been much work on Hilbert's tenth problem for the rings of integers of algebraic number fields .
13) The golden ratio is a fundamental unit of the algebraic number field __FORMULA__ and is a Pisot-Vijayaraghavan number.
14) Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory.
15) The problem for the ring of integers of algebraic number fields other than those covered by the results above remains open.
example sentences with algebraic number field
16) Dedekind zeta functions of algebraic number fields , which generalize the Riemann zeta function, often do have multiple complex zeros.17) Abelian varieties defined over algebraic number fields are a special case, which is important also from the viewpoint of number theory.
18) Let __FORMULA__ be an algebraic number field , called the base field, and let __FORMULA__ be a "field extension" of finite degree.
19) This way one can get back and forth between the algebraic number field "F" and its ring of integers "O""F".
20) The study of algebraic number fields , and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
21) As the laws of rational trigonometry give algebraic (and not transcendental) relations, they apply in generality to algebraic number fields beyond the rational numbers.
22) Due to the Galois correspondence between subgroups of Γ and algebraic number fields , the stabilizer corresponds to a field, the "field of moduli of the dessin".
23) On the automorphisms of the spectral completion of the algebraic numbers field , Journal of Pure and Applied Algebra, 212 (2008), 1427-1431.
24) If "A" is a Dedekind domain whose quotient field is an algebraic number field (a finite extension of the rationals) then shows that SK1("A") vanishes.
25) One of the classical results in algebraic number theory is that the ideal class group of an algebraic number field "K" is finite.
26) More generally, a prime of an algebraic number field "K" (also called a place) is an equivalence class of absolute values on "K".
27) Richard Dedekind's study of Lejeune Dirichlet's work was what led him to his later study of algebraic number fields and ideals.
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