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In 1989, Dipper and Jamed 2 extend the notion of a Schur algebra, see Green 8, to obtain the q-Schur algebra Sq(n,r). One of the main difficulties that can not be solved is to determine a suitable mathematical formula for the product between two elements in Sq(n,r), except for the mathmatical formua introduced by Green in 8 and the programming formula that supported this formula which is given 11 when q=1.