[ComputerGuru]

جبر, in transliteration, jabr, is the root of the word and the closest meaning is to bring (with a possible connotation of doing so against the entities natural inclination or state) back together parts (in healing).

To my mind, mathematically it would be closest to the literal concept of integration, but that is calculus and not what is generally considered to be algebra.

[agumonkey]

I associated al-jabr as classification. The 'back'ness felt more like bring back order by arranging same kinds on same sides.