large ideal


An ideal I of a ring R is called a large ideal if for every ideal J of R such that J≠{0}, I∩J≠{0}

A ring is semiprime iff every large ideal is dense.

Obviously all nontrivial ideal of an integral domainMathworldPlanetmath is a large ideal, and the maximal idealMathworldPlanetmath of any non-trivial local ringMathworldPlanetmath 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 2013-03-22 15:37:28
Last modified on 2013-03-22 15:37:28
Owner jocaps (12118)
Last modified by jocaps (12118)
Numerical id 12
Author jocaps (12118)
Entry type Definition
Classification msc 16D25