nil and nilpotent ideals
An element of a ring is nilpotent if for some positive integer .
A ring is nil if every element in is nilpotent. Similarly, a one- or two-sided ideal is called nil if each of its elements is nilpotent.
A ring [resp. a one- or two sided ideal ] is nilpotent if [resp. ] for some positive integer .
A ring or an ideal is locally nilpotent if every finitely generated subring is nilpotent.
The following implications hold for rings (or ideals):
Title | nil and nilpotent ideals |
Canonical name | NilAndNilpotentIdeals |
Date of creation | 2013-03-22 13:13:25 |
Last modified on | 2013-03-22 13:13:25 |
Owner | mclase (549) |
Last modified by | mclase (549) |
Numerical id | 6 |
Author | mclase (549) |
Entry type | Definition |
Classification | msc 16N40 |
Related topic | KoetheConjecture |
Defines | nil |
Defines | nil ring |
Defines | nil ideal |
Defines | nil right ideal |
Defines | nil left ideal |
Defines | nil subring |
Defines | nilpotent |
Defines | nilpotent element |
Defines | nilpotent ring |
Defines | nilpotent ideal |
Defines | nilpotent right ideal |
Defines | nilpotent left ideal |
Defines | nilpotent subring |
Defines | locally nilpotent |
Defines | locally nilpotent ring |
Defines | locally nilpo |