Re: determine maximal ideals

Li Yi wrote:

> This is my homework. I need some hints.
>
> Determine the maximal ideals of each of the following.
>
> (a) R x R;
> (b) R[x]/(x^2);
> (c) R[x]/(x^2-3x+2);
> (d) R[x]/(x^2+x+1).

What is R? A general ring? The field of real numbers?

If R_1 and R_2 are rings, the maximal ideals of R_1 x R_2
have the form M_1 x R_2 and R_1 x M_2 where M_i runs
through the maximal ideals of R_i.

If S is a ring, say S = R[x], and I is an ideal of S, then
the maximal ideals of S/I are the M/I where M runs
through the maximal ideals of S which contain I.

--
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Elegance is an algorithm"
Iain M. Banks, _The Algebraist_
.

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