algebraic number oor Viëtnamees

algebraic number

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(mathematics) A complex number that is a root of a polynomial equation with rational coefficients.

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complex number that is a root of a non-zero polynomial in one variable with rational coefficients
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In algebra, numbers are often represented by symbols called variables (such as a, n, x, y or z).
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By applying his construction to the sequence of real algebraic numbers, Cantor produces a transcendental number.
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His first construction shows how to write the real algebraic numbers as a sequence a1, a2, a3, ....
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Hilbert unified the field of algebraic number theory with his 1897 treatise Zahlbericht (literally "report on numbers").
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Algebraic number theory, in which the properties of numbers are studied from an algebraic point of view.
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The Disquisitiones covers both elementary number theory and parts of the area of mathematics now called algebraic number theory.
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The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century.
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Set theory, however, was founded by a single paper in 1874 by Georg Cantor: "On a Property of the Collection of All Real Algebraic Numbers".
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Kronecker objected to Cantor's proofs that the algebraic numbers are countable, and that the transcendental numbers are uncountable, results now included in a standard mathematics curriculum.
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Noether and a small team of students worked quickly through van der Waerden's 1930 book Moderne Algebra I and parts of Erich Hecke's Theorie der algebraischen Zahlen (Theory of algebraic numbers).
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The beginnings of algebraic number theory can be traced to Diophantine equations, named after the 3rd-century Alexandrian mathematician, Diophantus, who studied them and developed methods for the solution of some kinds of Diophantine equations.
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In modern algebra, unknown numbers are represented by letters, such as x or y.
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One of the founding works of algebraic number theory, the Disquisitiones Arithmeticae (Latin: Arithmetical Investigations) is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24.
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To be more general it can be done with algebraic symbols, but numbers are easier to understand.
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In the first (1908–1919), she made contributions to the theories of algebraic invariants and number fields.
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Noether's work Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern (Abstract Structure of the Theory of Ideals in Algebraic Number and Function Fields, 1927) characterized the rings in which the ideals have unique factorization into prime ideals as the Dedekind domains: integral domains that are Noetherian, 0- or 1-dimensional, and integrally closed in their quotient fields.
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Euler worked in almost all areas of mathematics, such as geometry, infinitesimal calculus, trigonometry, algebra, and number theory, as well as continuum physics, lunar theory and other areas of physics.
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While the visual nature of geometry makes it initially more accessible than other mathematical areas such as algebra or number theory, geometric language is also used in contexts far removed from its traditional, Euclidean provenance (for example, in fractal geometry and algebraic geometry).
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Countless results in number theory invoke the fundamental theorem of arithmetic and the algebraic properties of even numbers, so the above choices have far-reaching consequences.
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In the third epoch (1927–1935), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals.
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In the third epoch (1927–1935), Noether focused on noncommutative algebra, linear transformations, and commutative number fields.
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In November of the same year, Noether delivered a plenary address (großer Vortrag) on "Hyper-complex systems in their relations to commutative algebra and to number theory" at the International Congress of Mathematicians in Zürich.
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The Lie algebra of any compact Lie group (very roughly: one for which the symmetries form a bounded set) can be decomposed as a direct sum of an abelian Lie algebra and some number of simple ones.
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José Felipe Voloch (born 13 February 1963 in Rio de Janeiro) is a Brazilian mathematician who works on number theory and algebraic geometry.
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These texts deal with solving algebraic equations, and have led, in number theory to the modern notion of Diophantine equation.
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