For a long time, the editors of maths Wikipedia took objection to any 'simplifying' edits to make things more accessible, if they even slightly changed the meaning. Seems like a misunderstanding of what an encyclopedia is for, to me - overview first, expand afterwards. But I suppose mathematicians wouldn't be mathematicians if they weren't borderline obsessive. That first definition is probably more 'correct' although you're quite correct that it's almost unreadable.

Huh. Didn't think that a field needed to have division defined on it, at least not in the 'multiplication is the opposite of division' way you'd expect. Learn something new every day.