Testwiki:Reference desk/Archives/Mathematics/2007 March 1

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March 1

Apparently trivial abstract algebra problem

The following problem appears in my abstract algebra textbook (Hungerford):

Prove or disprove: Let R be a Euclidean domain; then $I=\{a\in R|\delta (a)>\delta (1_R)\}$ is an ideal in R.

This seems trivial to me: just take $R=\mathbb{Z}$ and $\delta (n)=|n|$; then I is not an ideal (it isn't even closed under addition). But the problem was in the "fairly hard" section, so I think I must be missing something. Maybe there's a typo? —Keenan Pepper 05:35, 1 March 2007 (UTC)

As I recall, in order for a subring of a Euclidean domain to be an ideal, it would absolutely have to contain 0; the I you describe above necessarily does not contain 0, hence cannot be an ideal. So no, I don't think you're missing something, I think it is just an easy problem. –King Bee ^{(T • C)} 14:00, 1 March 2007 (UTC)

Valuation of American Options Whaley Method

Hey, I'd like to have the derivation and equation for valuation of american options by the Whaley method.

Help with taking limits

i need help taking a limit as x goes to +0....of X^X^X....65.110.228.117 19:42, 1 March 2007 (UTC)State

You should do your own homework, as we won't do it for you here. Here is a hint. Start by trying to evaluate $\underset{x\to 0^{+}}{\lim }{x}^x$, and then use that result to evaluate the limit you actually want to evaluate. –King Bee ^{(T • C)} 19:45, 1 March 2007 (UTC)