**algebraic number** — n. a root of a polynomial equation with coefficients that are rational numbers … English World dictionary

**Algebraic number** — In mathematics, an algebraic number is a complex number that is a root of a non zero polynomial in one variable with rational (or equivalently, integer) coefficients. Complex numbers such as pi that are not algebraic are said to be transcendental … Wikipedia

**algebraic number** — Math. 1. a root of an algebraic equation with integral coefficients. 2. root1 (def. 10b). [1930 35] * * * real number for which there exists a polynomial equation with integer coefficients such that the given real number is a solution.… … Universalium

**algebraic number** — noun root of an algebraic equation with rational coefficients • Hypernyms: ↑irrational number, ↑irrational * * * noun : a root of an algebraic equation whose coefficients are rational * * * Math. 1. a root of an algebraic equation with integral… … Useful english dictionary

**algebraic number** — A real number that is the root of a polynomial equation. All rationals are algebraic (they are all roots of equations b x = a where a, b are integers). Reals that are not algebraic are called transcendental numbers … Philosophy dictionary

**algebraic number** — al′gebra′ic num′ber n. 1) math. a root of an algebraic equation with integral coefficients 2) math. root I, 9), b) • Etymology: 1930–35 … From formal English to slang

**algebraic number** — noun A complex number that is a root of a polynomial equation with rational coefficients. Ant: transcendental number … Wiktionary

**Algebraic number field** — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… … Wikipedia

**Algebraic number theory** — In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number… … Wikipedia

**algebraic number theory** — noun The subfield of number theory where algebraic numbers are studied using algebra … Wiktionary