Originally Posted by Muezzin
Yes, you are right about the origin of the word algebra, the spelling is al-jabr.
The first writings and algebraic formulas were devised by Diophantus of Alexandria(Egypt) in the 3rd century AD.
Religion in Egypt at this time was a strange combination of ancient Egyptian mythology (ie. Ra sun-god), worship of deities in animal form (ie. cats, hawks, bulls), and greek, Jewish, and christian concepts. A lot of influence was due to the fact that Egypt was a roman province at this time.
Again though, islam was not founded yet for a few hundred years, so algebra is an arab invention, not a muslim invention. Perhaps some credit could go to egyptian mythology(joking).
Algebra was brought from ancient Babylon, Egypt and India to Europe via Italy by the Arabs.