Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20080804 06:56:36#2 20080804 08:50:34#3 20080804 11:44:27
Re: IdealsA ring R is a field if and only if it's only ideals are 0 and R. In other words, fields aren't interesting in Ideal Theory. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #4 20080804 12:05:25
Re: Ideals
Last edited by JaneFairfax (20080804 20:06:26) #5 20080804 12:31:38#6 20080804 12:56:46#7 20080804 13:04:07
Re: IdealsLet k be an algebraically closed field. M is a maximal ideal in the polynomial ring k[x_1, x_2, ..., x_n] if and only if M = (x_1  a_1, ..., x_n  a_n) for some a_1, ..., a_n in k. Last edited by Ricky (20080804 13:14:01) "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20080805 15:16:37
Re: IdealsThe proof of the theorem in post #4 is a lot more straightforward if you use a bit more of the machinery. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20080806 00:39:15#10 20080806 01:20:59
#11 20080806 01:42:02
