Let S be a completely 0 -simple semigroup and F be an algebraically closed field. Then for each 0 -minimal right ideal M of S , M = B ∪ C ∪ { 0 } , where B is a right group and C is a zero semigroup. Also, a matrix representation for S other than Rees matrix is found for the condition that the semigroup ring R ( F , S ) is semisimple Artinian.