Word.ws English Dictionary

algebraic integer

algebraic integer noun: a real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.

Noun

algebraic integer (plural algebraic integers)

  1. A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
    • A Gaussian integer z=a+ib is an algebraic integer since it is a solution of either the equation z²+(-2a)z+(a²+b²)=0 or the equation z-a=0.
    • An algebraic number is said to be an algebraic integer if the coefficient of the highest power of x in the minimal polynomial P is 1. The algebraic integers in an algebraic number field k form a ring R.1984, Alan Baker, A Concise Introduction to the Theory of Numbers, Cambridge University Press, page 62

algebraic integer meaning in Tamil

algebraic integer in Tamil

இயற்கணித முழு எண்

Forms of algebraic integer

pluralalgebraic integers

Questions about algebraic integer

What does algebraic integer mean?
Algebraic integer means a real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.
What is algebraic integer in Tamil?
Algebraic integer in Tamil is இயற்கணித முழு எண். See Algebraic integer meaning in Tamil.
What part of speech is algebraic integer?
Algebraic integer is a noun.
What is the plural of algebraic integer?
The plural of algebraic integer is algebraic integers.

Words near algebraic integer in the dictionary

  1. algebraic geometry
  2. algebraic graph theories
  3. algebraic graph theory
  4. algebraic group
  5. algebraic groups
  6. algebraic integer
  7. algebraic integers
  8. algebraic K-theory
  9. algebraic normal form
  10. algebraic notation
  11. algebraic notations

Source and license

Adapted from Wiktionary: algebraic integer (page history and authors); algebraic integer (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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