Talk:Diagonal Complement Relation Compatible with Group Operation

The whole "compatible with operation" thing is kind of awkward. We do have Definition:Ordering Compatible with Ring Structure, so maybe we should add pages like that for algebraic structures, groups, and fields? --Dfeuer (talk) 23:59, 6 January 2013 (UTC)

Once you've demonstrated under what conditions a relation is compatible with an operation, why do you need to consider separately the operation in the various structures? Surely if a result holds for a general operation, it's then immaterial what structures that operation is on?

And unless you need to redefine the definition, you don't get relations "compatible with group" or "compatible with field" etc, it's an *operation* it's compatible with, not a *structure*. If I'm wrong and you have documentary evidence backing up this usage, feel free to add this different usage to the definition. --prime mover (talk) 06:15, 7 January 2013 (UTC)