Equivalence classes in rings

1. Jan 24, 2008

InquilineKea

So I'm kind of confused about the definition:

$$a-b\in I$$

Why a - b instead of a + b?

2. Jan 24, 2008

waht

Are you trying to prove that a-b is an equivalence relation? Can you be more specific?

Last edited: Jan 24, 2008
3. Jan 24, 2008

morphism

It's actually natural to write a-b because I becomes zero when you quotient out by it, so a-b in I means a-b=0 or, written differently, a=b.

4. Jan 27, 2008

mathwonk

you would presumably want a equivalent to a, which follows from a-a in I, rather than a+a in I.