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al khawrzmi
Yes, they did take a part in it, but it wasn't as strong and as practical as the Arabic algebra which was founded later.
many say that algebra was founded by diophantus but actually al- khwarizmi wrote about algebra [al- jabr] in his book 'compendious book on calculation by completion and balancing.'
In the context where algebra is identified with the theory of equations, the Greek mathematician Diophantus has traditionally been known as the "father of algebra" but in more recent times there is much debate over whether al-Khwarizmi, who founded the discipline of al-jabr, deserves that title instead.
foundations algebra is probably pre algebra, which is before algebra, so no.