Suppose that R is a Euclidean domain and a ∈ R is a non-zero non-unit.
For an element b ∈ R consider the subset bR/aR = {r + Ra : r ∈ bR} of R/aR.
Let r + Ra, s + Ra ∈ bR/aR so that r, s ∈ bR, then r + s ∈ bR which gives (r + Ra) + (s + Ra) = (r + s) + Ra ∈ bR/aR.
Let r ∈ Ra ∈ R/aR and s + Ra ∈ bR/aR so that s ∈ bR, then rs ∈ bR implies that (r + Ra) · (s + Ra) = (rs) + Ra ∈ 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?