large ideal
An ideal $I$ of a ring $R$ is called a large ideal if for every ideal $J$ of $R$ such that $J\ne \{0\}$, $I\cap J\ne \{0\}$
A ring is semiprime iff every large ideal is dense.
Obviously all nontrivial ideal of an integral domain^{} is a large ideal, and the maximal ideal^{} of any nontrivial local ring^{} is a large ideal.
References

1
N.J. Fine, L. Gillman, J. Lambek,
”Rings of Quotients of Rings of Functions”,
Transcribed and edited into PDF from the original 1966 McGill University Press book
(see http://tinyurl.com/24unqshere, Editors: M. Barr, R. Raphael),
http://tinyurl.com/ytw3tjOnline download, Accessed 24.10.2007
Title  large ideal 

Canonical name  LargeIdeal 
Date of creation  20130322 15:37:28 
Last modified on  20130322 15:37:28 
Owner  jocaps (12118) 
Last modified by  jocaps (12118) 
Numerical id  12 
Author  jocaps (12118) 
Entry type  Definition 
Classification  msc 16D25 