large ideal
An ideal of a ring is called a large ideal if for every ideal of such that ,
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 non-trivial 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