Question on Ideals (Algebraic Geometry)

[arunma]

I have a question for anyone who is knowledgeable in algebra. What does it mean for one ideal to be "strictly bigger" than another?

 

[mathwonk]

An ideal I strictly bigger than the ideal J iff J is a proper subset of I.

at least that's what i think.

this is such a trivial question that it must not be the real question. I.e. what is the context for this question and why is it puzzling you?

 

[arunma]

Yes, I suppose that was a trivial question. Indeed the answer you provided is also given in my book. I suppose what I should have asked is: what does it "mean" for one ideal to be strictly larger than another. In particular, if the terms in one ideal are not divisible by the terms in a second ideal, does this make the first ideal larger?

I'm sorry that I am phrasing my questions rather imprecisely. But I don't take algebra courses very often (I generally favor analysis), so I'm still trying to figure out precisely what ideals are and why they are of interest to mathematicians. I'd be very interested to hear any insight you've got on this.

 

[mathwonk]

these quesyions are more interesting:

1) what does it mwean geometrically for an ideL TO BE larger?

2) how does one check LGEBRAICALLY THt AN IDEAL generated by a given finites et of elements, is indeed lakrger thAN AN IDEAL generate dby anoither finite set of elements?

these are not so easy. i know somethings about them but i will answer later.