Maybe there is a Language confusion here.
In english, divided has the following definition
http://www.thefreedictionary.com/divideddi·vid·ed (d-vdd)
adj.
1. Separated into parts or pieces.
2. Being in a state of disagreement or disunity: a divided nation.
3. Moved by conflicting interests, emotions, or activities: divided loyalties.
4. Separated by distance: a child divided from her familiar surroundings.
5. Having the lanes for opposing traffic separated: divided highways.
6. Botany Having indentations extending to the midrib or base and forming distinct lobes: divided leaves
The sentence "Divided by Element of the Pillar/Tower." does not make any gramatical sence.
In relation to your example: you have targeted the Air pillar and a creature so the creature gains the ability of the Air Alchemy card in this case ignite. For the Aether Pillar I assume the creature would gain the ability to grant Immortality to creatures. In any case there is no division of anything so I cannot work out what is being divided.
In all sence you cannot divide anything into an undefined non-numerical way.