Tip. You can look up words, expressions, names, titles...

# Algebraic number

## Definition of the noun algebraic number

What does algebraic number mean as a name of something?

noun

1. root of an algebraic equation with rational coefficients
• lexical domain: Quantities - nouns denoting quantities and units of measure
• more generic terms: irrational / irrational number = a real number that cannot be expressed as a rational number

## Explanation

Algebraic number: In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients. Numbers such as π that are not algebraic are said to be transcendental. Almost all real and complex numbers are transcendental.

• also known as 代數數

## Printed dictionaries and other books with definitions for Algebraic number

Click on a title to look inside that book (if available):

### Encyclopaedia of Mathematics (2012)

by Michiel Hazewinkel

A complex number is called an algebraic number over a field PCC if it is a root of a polynomial (1) with coefficients from P. The minimal polynomial, the degree over P and the conjugate numbers over P for algebraic numbers over P are defined ...

### The VNR Concise Encyclopedia of Mathematics (2012)

by S. Gottwald

Let } be an algebraic number. The smallest field k = Q(3) that contains Q and also 8 is called an algebraic number field. For example, Q(V3) consists of all numbers of the form a + b V3, where a and b are rational numbers. It is easy to check ...

### MCGRAW-HILL DICTIONARY OF MATHEMATICS, 2/E (2002)

by McGraw-Hill Education

algebraic number Any root of a polynomial with rational coefficients. { :al-je:bra-ik 'nom-bor } algebraic number field A finite extension field of the field of rational numbers. { :aljoibra-ik 'nom-bor ,feld } algebraic number theory The study of ...

### Encyclopedia of Cryptography and Security (2014)

by Henk C.A. van Tilborg, Sushil Jajodia

Signatures AHS Competition/SHA- Alberti Encryption Algebraic Immunity of Boolean Functions Algebraic Number Field Algorithmic Complexity Attacks Algorithmic DoS Alphabet Android's Security Framework–Understanding the Security ...

### The Mathematics Dictionary (1992)

by R.C. James, Glenn James

algebraic number. (1) Any ordinary positive or negative number; any real directed number. (2) Any number which is a root of a polynomial equation with rational coefficients; the degree of the polynomial is said to be the ...

### The New Volumes of the Encyclopaedia Britannica (1902)

Constituting in Combination with the Existing Volumes of the Ninth Edition, the Tenth Edition of that Work, and Also Supplying a New, Distinctive, and Independent Library of Reference Dealing with Recent Events and Developments

Every algebraic number can be expressed in the form osa, where a0 is a natural number and to an algebraic integer; in all that follows it will be supposed that a = 1, and consequently () is integral. Associated with 6 we have a corpus Q = R(0) ...

### The Encyclopedia Britannica (1922)

a dictionary of arts, sciences, literature and general information by Hugh Chisholm

There is a corresponding theory for the " prime ideals " of the " corpus " associated with any algebraic number. The ana- luguc of Riemann's zeta- function was discovered by R. Dcdekind, but it is only recently that, in the hands of E. Hecke and ...

### The Century Dictionary: The Century dictionary (1911)

Algebraic number, a root of ...

### The Century Dictionary and Cyclopedia: The Century dictionary ... prepared under the superintendence of William Dwight Whitney ... rev. & enl. under the superintendence of Benjamin E. Smith (1914)

by William Dwight Whitney, Benjamin Eli Smith

See abundant — Algebraic number, a root of an algebraic equation with whole numbers for its coefficients. -— Alternate, amicable, apocalyptic, appllcate, artificial numbers. See the adjectives. — A number of, several; sometimes, many: as, ...

## Online dictionaries and encyclopedias with entries for Algebraic number

Click on a label to prioritize search results according to that topic: