Modular ideal
From Encyclopedia of Mathematics
A right (left) ideal 
of a ring 
having the following property: There is at least one element 
in 
such that for all 
from 
the difference 
belongs to 
(respectively, 
). The element 
is called a left (right) identity modulo the ideal 
. In a ring with identity every ideal is modular. Every proper modular right (left) ideal can be imbedded in a maximal right (left) ideal, which is automatically modular. The intersection of all maximal modular right ideals of an associative ring coincides with the intersection of all maximal left modular ideals and is the Jacobson radical of the ring. Modular ideals are also called regular ideals.
References
| [1] | N. Jacobson, "Structure of rings" , Amer. Math. Soc. (1956) |
How to Cite This Entry:
Modular ideal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Modular_ideal&oldid=31546
Modular ideal. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Modular_ideal&oldid=31546
This article was adapted from an original article by K.A. Zhevlakov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article