Suppose that R is a Euclidean domain and a âˆˆ R is a non-zero non-unit.

For an element b âˆˆ R consider the subset bR/aR = {r + Ra : r âˆˆ bR} of R/aR.

Let r + Ra, s + Ra âˆˆ bR/aR so that r, s âˆˆ bR, then r + s âˆˆ bR which gives (r + Ra) + (s + Ra) = (r + s) + Ra âˆˆ bR/aR.

Let r âˆˆ Ra âˆˆ R/aR and s + Ra âˆˆ bR/aR so that s âˆˆ bR, then rs âˆˆ bR implies that (r + Ra) Â· (s + Ra) = (rs) + Ra âˆˆ bR/aR.

Hence bR/aR is an ideal in R/aR

Just in case you weren’t sure that it was.

It’s almost 2 am, what do you expect?

Oh, and I goofed while writing a game theory midterm last week, and only got 92/100.

I forgot to do part II of question 1, inspite of the note on the test paper saying “Don’t forget to do part (ii) below”.

Argh!

Oh, and should I do a blurb on the math behind error correction, specifically, as it’s implemented on CDs?