i guess i am talking modulo 2 math. or whatever it is you use for CRC codes.
Yeah, Z[sub]2[/sub].
<pedantry>
There is a notion of additive inverse, it’s just that every element is its own inverse.
Z[sub]2[/sub] is a Boolean algebra, but is hardly the only. Your nickname tells me you already knew this, though.
</pedantry>
Is anyone going to torture the OP by explaining how mathematically Halloween is equal to Christmas?
In general boolean algebras, there’s no notion of an inverse of either operation, at least not in the usual sense. You can get an both inverses in a two-element boolean algebra, but nowhere else.
Actually, I’m going to have to disagree with you here. Z[sub]2[/sub] is only a boolean algebra in the same sense that R is a well-ordered set: you can get it to be one, but you have to disregard the normal structure.
- corresponds to [symbol]Ù[/symbol], but + does not correspond to [symbol]Ú[/symbol] because it is not the case that a + b > a for all a, b.
Check Mathworld for a reference on why you’d need that.
I like math. 
Oh, of course I assumed you’d meant that. Actually, looking back I think it was your comma that confused me.
I read that sentence with a comma as using “or Z[sub]2[/sub]” effectively as an appositive. That is, I read “are you talking about a Boolean algebra (in other words: Z[sub]2[/sub])?” rather than “are you talking about something which is either a Boolean algebra or Z[sub]2[/sub]?”