algebraic integer
Let be an extension (http://planetmath.org/ExtensionField) of contained in . A number is called an algebraic integer of if it is the root of a monic polynomial with coefficients in , i.e., an element of that is integral over . Every algebraic integer is an algebraic number (with ), but the converse is false.
Title | algebraic integer |
Canonical name | AlgebraicInteger |
Date of creation | 2013-03-22 11:45:41 |
Last modified on | 2013-03-22 11:45:41 |
Owner | KimJ (5) |
Last modified by | KimJ (5) |
Numerical id | 13 |
Author | KimJ (5) |
Entry type | Definition |
Classification | msc 11R04 |
Classification | msc 62-01 |
Classification | msc 03-01 |
Related topic | IntegralBasis |
Related topic | CyclotomicUnitsAreAlgebraicUnits |
Related topic | FundamentalUnits |
Related topic | Monic2 |
Related topic | RingWithoutIrreducibles |