<Ul> <Li> An identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a . </Li> <Li> Every element has an inverse: for every member a of S, there exists a member a such that a ∗ a and a ∗ a are both identical to the identity element . </Li> <Li> The operation is associative: if a, b and c are members of S, then (a ∗ b) ∗ c is identical to a ∗ (b ∗ c). </Li> </Ul> <Li> An identity element e exists, such that for every member a of S, e ∗ a and a ∗ e are both identical to a . </Li> <Li> Every element has an inverse: for every member a of S, there exists a member a such that a ∗ a and a ∗ a are both identical to the identity element . </Li> <Li> The operation is associative: if a, b and c are members of S, then (a ∗ b) ∗ c is identical to a ∗ (b ∗ c). </Li>

Who contributed to the development of algebra and in what capacity