every ring is an integer algebra
Let R be a ring. Then R is also an algebra over the ring of integers if we define the action of ℤ on R by the following rules:
0⋅x=0 |
(n+1)⋅x=n⋅x+x |
(-n)⋅x=-(n⋅x) |
In other words, the action of a positive integer n on x is to add x to itself n times and the action of a negative integer n on x is to subtract x to itself n times.
Title | every ring is an integer algebra |
---|---|
Canonical name | EveryRingIsAnIntegerAlgebra |
Date of creation | 2013-03-22 14:47:47 |
Last modified on | 2013-03-22 14:47:47 |
Owner | rspuzio (6075) |
Last modified by | rspuzio (6075) |
Numerical id | 5 |
Author | rspuzio (6075) |
Entry type | Example |
Classification | msc 13B99 |
Classification | msc 20C99 |
Classification | msc 16S99 |
Related topic | GeneralAssociativity |