Isomorphisms
Mar. 6th, 2002 10:12 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
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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.
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.
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Date: 2002-03-06 11:42 am (UTC)