multiplicative filter

For any ring A, any set SA and any element xA, we use the notation


Let A be a commutative ring with unity, and let (A) be the set of all ideals of A.

  • A Multiplicative Filter of A is a filter on (A) such that I,JIJ.

  • A Gabriel Filter of A is a filter on (A) such that

    [I,J(A) and xI,(J:x)]J

Note that Gabriel Filters are also Multiplicative Filters.

Title multiplicative filter
Canonical name MultiplicativeFilter
Date of creation 2013-03-22 16:48:22
Last modified on 2013-03-22 16:48:22
Owner jocaps (12118)
Last modified by jocaps (12118)
Numerical id 6
Author jocaps (12118)
Entry type Example
Classification msc 03E99
Classification msc 54A99
Defines Gabriel Filter
Defines Multiplicative Filter