@Setanta,
First of all, i wanna tell you something about Ibraham's god (or god of ibrahim that he made ), Judaism, Christianity, Islam and Baha'i Faith are sometimes called "Abrahamic religions", because they all accept the tradition that God (Hebrew: יהוה Yahweh or YHWH (see Tetragrammaton), often rendered as Jehovah (יְהֹוָה) in English; Arabic: الله Allah; Aramaic: Elah or Alaha) revealed himself to the patriarch Abraham. (http://en.wikipedia.org/wiki/God_in_Abrahamic_religions) , but at the during of the time it change's to allah for example The numerous names for god have been a source of debate among biblical scholars.
Elohim (god, or authority, plural form),
El (mighty one), El Shaddai (almighty), Adonai (master), Elyon (highest), Avinu (our father), are regarded by many religious Jews not as names, but as titles highlighting different aspects of YHWH and
the various 'roles' of God, and as you know alla (الی له) sound's just like allah or allakh(ال اه), but anyway you know it, mohammad and Moses are from Abrahim's family!
And about the exist and my definition for god! I should say, first i said i have no strictly idea and i'm here for understand new idea for myself, Also i said god(on my believe) is allah because i think it is perfect and complete, as for a good definition for god or allah i can say , the god is reality of exist not self-exist as i know, and this
reality of exist will require the quality and adjectives of god( the long list!!!!), and it is marvelous truth about the god is that the nature is manifestation of God.