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

rar

[kitty-goth.livejournal.com]

That's one of those isomorphisms that I can just *see*

That rocks.

[zotz]

Gesundheit.

[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

[zz]

if only my brain didn't automatically reject mathematical concepts it can't immediately visualise or see a use for.. :(

[ladycat.livejournal.com]

I read this as "Sex & Groups"

I wonder if polynominals are related to polyamory ;p

Cat - who struggles with long divsion