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):

### Historical Encyclopedia of Natural and Mathematical Sciences (2009)

by Ari Ben-Menahem

The failure of 18th and 19th century mathematics to resolve Format's Last " Theorem" led to the development of the new arithmetic of algebraic numbers. An algebraic number is a complex number that is a root of an algebraic equation p(x) = 0, ...

### The Penguin Dictionary of Mathematics (2008)

Fourth edition by David Nelson

algebraic number A number, real or complex, that is the *root of a *polynomial equation with ...

### Encyclopaedia of Mathematics (2013)

A-Integral — Coordinates by M. 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 Concise Oxford Dictionary of Mathematics (2009)

by Christopher Clapham, James Nicholson, James R. Nicholson

algebraic number A real number that is the root of a *polynomial equation ...

### 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 ...

### Academic Press Dictionary of Science and Technology (1992)

by Christopher G. Morris, Academic Press

algebraic number Mathematics, a root of a polynomial with rational coefficients. algebraic number field Mathematics, any extension ...

### Van Nostrand’s Scientific Encyclopedia (2013)

by Douglas M. Considine, Glenn D. Considine

An algebraic number field R(6) of degree n is generated by the root 6 of an algebraic equation aox" + aix" +...

### 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 ...

### 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

Algebraic Number Field. A.

### The Encyclopaedia Britannica (1902)

A Dictionary of Arts, Sciences, and General Literature

6"-" are said to form a set of conjugate algebraic numbers of the nth order. If a = 1, the roots are said to form a set of conjugate algebraic integers. Every algebraic number can be expressed in the form osa, where a0 is ...

### 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) ...

## Online dictionaries and encyclopedias with entries for Algebraic number

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