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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)[reply]

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)[reply]

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[reply]

You should do your own homework, as we won't do it for you here. Here is a hint. Start by trying to evaluate

\lim _{x\to 0^{+}}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)[reply]