unit
Let be a ring with multiplicative identity . We say that is an unit (or unital) if divides (denoted ). That is, there exists an such that .
Notice that will be the multiplicative inverse (in the ring) of , so we can characterize the units as those elements of the ring having multiplicative inverses.
In the special case that is the ring of integers of an algebraic number field , the units of are sometimes called the algebraic units of (and also the units of ). They are determined by Dirichlet’s unit theorem.
Title | unit |
Canonical name | Unit |
Date of creation | 2013-03-22 11:56:28 |
Last modified on | 2013-03-22 11:56:28 |
Owner | drini (3) |
Last modified by | drini (3) |
Numerical id | 15 |
Author | drini (3) |
Entry type | Definition |
Classification | msc 16B99 |
Synonym | unital |
Related topic | Associates |
Related topic | Prime |
Related topic | Ring |
Related topic | UnitsOfQuadraticFields |
Defines | algebraic unit |