What does algebraic integer mean?
Definitions for algebraic integer
al·ge·bra·ic in·te·ger
This dictionary definitions page includes all the possible meanings, example usage and translations of the word algebraic integer.
Wiktionary
algebraic integernoun
A number (real or complex) which is a root of a monic polynomial whose coefficients are integers.
Wikidata
Algebraic integer
In number theory, an algebraic integer is a complex number that is a root of some monic polynomial with coefficients in ℤ. The set of all algebraic integers is closed under addition and multiplication and therefore is a subring of complex numbers denoted by A. The ring A is the integral closure of regular integers ℤ in complex numbers. The ring of integers of a number field K, denoted by OK, is the intersection of K and A: it can also be characterised as the maximal order of the field K. Each algebraic integer belongs to the ring of integers of some number field. A number x is an algebraic integer if and only if the ring ℤ[x] is finitely generated as an abelian group, which is to say, as a ℤ-module.
Numerology
Chaldean Numerology
The numerical value of algebraic integer in Chaldean Numerology is: 1
Pythagorean Numerology
The numerical value of algebraic integer in Pythagorean Numerology is: 1
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"algebraic integer." Definitions.net. STANDS4 LLC, 2024. Web. 19 Apr. 2024. <https://www.definitions.net/definition/algebraic+integer>.
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