Isomorphisms

[ciphergoth]

For kitty_goth and gothslut, though others (eg ajva) may also be interested - a brief description of what I was going on about in the pub the other day. This is from "Sets and Groups", J A Green, Example 200.

In the ring R[X] of polynomials over the reals, consider the principal ideal J generated by the polynomial (X^2 + 1). Then the quotient ring R[X]/J is isomorphic to the field C of complex numbers: the map theta: C -> R[X]/J s.t. theta(a + bi) = a + bX + J is a ring-isomorphism.

Comments

[pure-mourning.livejournal.com]

You know, I was just trying to explain the same thing to a friend of mine.

But I like your wording better :)

C
x

[ciphergoth.livejournal.com]

This is the thing I found myself trying to explain to gothslut while we were in bed together. When I'd finished, she grabbed me and kissed me - so either she was trying to shut me up or quotient ring isomorphisms are sexy :-)

Re:

[pure-mourning.livejournal.com]

While math does turn me on, as I'm sure it does everyone, I think it's more the raw intelligence part that's sexy and the way you boys sort of trail off into your own worlds while explaining something. I nearly broke into tears of love the time K so gently taught me html..

But I am a bit weird.

P.S. Add me so I can see you on my new journal/friends page ;) goth_christine is no more.

[wechsler.livejournal.com]

Well she *did* wait for you to finish then... which probably says more about her patience than, erm, the stuff I didn't understand ;)