1. Also, any constructible number is an algebraic number.

2. See also algebraic number field.

3. The answer is always an algebraic number.

4. Algebraic number theory studies various number rings that generalize the set of integers.

5. Number theory, field theory, algebraic geometry, algebra, group theory

6. Commutative algebra is essentially the study of the rings occurring in algebraic number theory and algebraic geometry

7. Kresa was the first to introduce algebraic number to trigonometry.

8. A separate inspiration for F1 came from algebraic number theory.

9. The complex number qdχ(g)/n is an algebraic integer.

10. He works in algebraic geometry, representation theory, and number theory.

11. Further branches crucially applying groups include algebraic geometry and number theory.

12. Let X be an algebraic variety defined over a number field.

13. He also wrote on algebraic geometry, number theory, and integral equations.

14. In algebraic number theory, the rings of algebraic integers are Dedekind rings, which constitute therefore an important class of Commutative rings.

15. The rough subdivision of number theory into its modern subfields—in particular, analytic and algebraic number theory.

16. Using tools of algebraic number theory, Andrew Wiles proved Fermat's Last Theorem.

17. He has contributed to number theory and related parts of algebraic geometry.

18. This is one of the main results of classical algebraic number theory.

19. Class field theory is a branch of algebraic number theory which seeks to classify all the abelian extensions of a given algebraic number field, meaning Galois extensions with abelian Galois group.

20. In this section, we want to show that the class number of an algebraic number field is finite.

21. He took up Waring's problem in algebraic number fields and got interesting results.

22. The value of K(a, b; m) is always an algebraic real number.

23. As in algebraic notation, each cell is identified by a letter+number combination.

24. So given a particular complex number α one can ask how close α is to being an algebraic number.

25. The Disquisitiones covers both elementary number theory and parts of the area of mathematics now called algebraic number theory.

26. However, an algebraic function of several variables may yield an algebraic number when applied to transcendental numbers if these numbers are not algebraically independent.

27. The same objects can be studied using methods from algebraic geometry, module theory, analytic number theory, differential geometry, operator theory, algebraic combinatorics and topology.

28. Aside from his work in algebraic number theory he wrote a great number of Japanese textbooks on mathematics and geometry.

29. The Stufe of an algebraic number field is ∞, 1, 2 or 4 ("Siegel's theorem).

30. — We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields.

31. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals.

32. It is not known whether Khinchin's constant is a rational, algebraic irrational or transcendental number.

33. Importantly, the same number of curves is obtained as one naively expects from algebraic geometry.

34. ‘Fermat preferred the Algebraic techniques that he used to such devastating effect in number theory.’ ‘His work in Algebraic number theory led him to study the quaternions and generalisations such as Clifford algebras.’ ‘This gave powerful results such as a purely Algebraic proof of the Riemann Roch theorem.’

35. Algebraic (comparative more Algebraic, superlative most Algebraic) Of, or relating to, algebra

36. We discuss here some basic problems of algebraic number theory under a computational point of view.

37. Williams developed algorithms for calculating invariants of algebraic number fields such as class numbers and regulators.

38. Kronecker wrote his 1845 dissertation, at the University of Berlin, on number theory , giving special formulation to units in certain algebraic number fields .

39. At the University of Uppsala, Harald Bergström did research mainly on algebraic number fields and related topics.

40. In the first (1908–1919), she made contributions to the theories of algebraic invariants and number fields.

41. In this way, Gauss arguably made a first foray towards both Évariste Galois's work and algebraic number theory.

42. Another example, playing a key role in algebraic number theory, is the field Qp of p-adic numbers.

43. In mathematics, an Algebraic expression is an expression built up from integer constants, variables, and the Algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

44. For instance, algebraic topology uses algebraic objects to study topologies.

45. Today, one of the most important branches of pure mathematics is algebraic number theory, which studies rational numbers (fractions).

46. The method encompasses a new one-way function with trapdoor based on Artin reciprocity in an algebraic number field.

47. All those totally real algebraic number fieldsK of degreen=4 will be studied which have a quadratic subfield Ω.

48. Lejeune Dirichlet's lectures on number theory were edited and extended by Richard Dedekind, who used Euclid's algorithm to study algebraic integers, a new general type of number.

49. Covered subject areas include simplification and evaluation of algebraic expressions, proof of algebraic identities, solution of algebraic equations and inequalities.

50. One of the major achievements in algebraic number theory and algebraic geometry of the twentieth century was to find the correct formulations of the corresponding theory for abelian varieties of dimension d > 1.

51. His research interests are Algebraic Geometry and Number Theory (in particular Diophantine Approximation and Transcendence Theory) and Hodge Theory (Periods).

52. Marc Krasner (1912 – 13 May 1985, in Paris) was a Russian-born French mathematician, who worked on algebraic number theory.

53. Working with Hasse, he dealt with algebraic number theory and produced a script of Hassen's lecture on class-field theory.

54. The algebraic sign of the number shall be disregarded during the rounding procedure; e.g. 1.57 becomes 1.6; -1.57 becomes -1.6.

55. Fulton is known as the author or coauthor of a number of popular texts, including Algebraic Curves and Representation Theory.

56. Adams made a number of important theoretical advances in algebraic topology, but his innovations were always motivated by specific problems.

57. These texts deal with solving algebraic equations, and have led, in number theory to the modern notion of Diophantine equation.

58. Analyzing Concavity (algebraic) …

59. Algebraic Expressions Calculator

60. Geometry, algebraic topology

61. Another way of generalizing ideas from algebraic geometry is differential algebraic geometry.

62. An algebraic expression is one or more algebraic terms in a phrase.

63. If we modify the algebraic structure of the network the same algorithm can be applied to large number of other problems.

64. The algebraicity criterion above follows from a more basic algebraicity criterion concerning smooth formal germs in algebraic varieties over number fields.

65. It is shown that such symbolic algebraic thinking includes finding an algebraic approach, acting intentionally in an algebraic way, and reflecting algebraically.

66. The Algebraic multiplicity of an eigenvalue \(\lambda\) of \(A\) is the number of times \(\lambda\) appears as a root of \(p_A\)

67. As Murty's survey paper notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry".

68. An Abelian variety is an algebraic group that is a complete algebraic variety

69. Generalized algebraic data types.

70. Algebraic Geometry, Sendai 1985.

71. Allen Hatcher, Algebraic topology.

72. AMS translations 1966 (Mordell conjecture for function fields) Manin: Algebraic topology of algebraic varieties.

73. Project papers have been published on functional codes arising from the intersections of algebraic hypersurfaces of small degree with a non-singular quadric, and on bounds on the number of rational points of algebraic hypersurfaces over finite fields.

74. In algebraic geometry over any field, by analogy, it also happens in algebraic codimension one.

75. Evaluating simple algebraic expressions, addition, subtraction, multiplication and division, use of brackets, simple algebraic fractions;

76. ALNUSET has three fully integrated environments: the Algebraic Line, the Algebraic Manipulator, and the Functions.

77. In addition to mathematical physics, he works on algebraic geometry, category theory, and algebraic topology.

78. This work anticipates a number of later theories, such as the general theory of algebraic correspondences, Hecke operators, and Lefschetz fixed-point theorem.

79. Susan Howson (born in 1973) is a former British mathematician whose research was in the fields of algebraic number theory and arithmetic geometry.

80. Algebraic topology at Indiana University