The phrase "algebraic number" is correct and usable in written English.
It is typically used in mathematics to refer to a complex number that is a root of a non-zero polynomial equation with rational coefficients.
Example: "The number √2 is an algebraic number because it is a solution to the equation x² - 2 = 0."
Alternatives: "algebraic integer" or "algebraic expression".
More generally, field extensions provide another class of examples of vector spaces, particularly in algebra and algebraic number theory: a field containing a smaller field is an -vector space, by the given multiplication and addition operations of.
They proved two important theorems: a local-global theorem stating that if a finite-dimensional central division algebra over a number field splits locally everywhere then it splits globally (so is trivial), and from this, deduced their Hauptsatz ("main theorem"): every finite dimensional central division algebra over an algebraic number field F splits over a cyclic cyclotomic extension.
Bhargava's area is algebraic number theory, which mixes algebra with the study of the properties of numbers.
This law became, and remains, a central tool in algebraic number theory.
In 1934 Gelfond proved that ab is transcendental if a is an algebraic number not equal to 0 or 1 and if b is an irrational algebraic number.
Deligne's work provided important insights into the relationship between algebraic geometry and algebraic number theory.
In 1955 Roth showed that μ̄ = 2 for any algebraic number α.
He developed the general theory of units in algebraic number theory.
Along with classical and analytic number theory, scholars now explored specialized subfields such as algebraic number theory, geometric number theory, and combinatorial number theory.
Although number fields are fundamental objects in algebraic number theory, some basic facts are unknown, such as how many number fields there are for a fixed degree and fixed discriminant.
In 1988 he received the Wolf Prize in Mathematics "for outstanding work combining topology, algebraic and differential geometry, and algebraic number theory; and for his stimulation of mathematical cooperation and research".
