Re: Intersection of Ideals
- From: rusin@xxxxxxxxxxxxxxxxxxxxx (Dave Rusin)
- Date: 9 May 2006 06:40:19 GMT
In article <1147119131.092269.316010@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<trusiki@xxxxxxxxx> wrote:
Prove that if A and B are primary ideals belonging to the same prime
ideal P then
(A intersection B) is a primary ideal belonging to P.
Arguably, the whole point to having ideals in rings is so that you
can form quotient rings. Different kinds of ideals get a special
name because the corresponding quotient rings havs a special feature
(e.g. they are fields, or integral domains). Well, what characterizes
primary rings in this way? How is the correponding prime related to
the primary ideal in this way?
With all this fixed in your mind, just apply the homomorphism
R/(A \cap B) --> (R/A) + (R/B) .
dave
.
- References:
- Intersection of Ideals
- From: trusiki
- Intersection of Ideals
- Prev by Date: Re: Polynomials of degree 2 with odd coefficients
- Next by Date: Blaschke product+asymptotic
- Previous by thread: Re: Intersection of Ideals
- Next by thread: Intersection of Ideals
- Index(es):
Relevant Pages
|
