sums of units in baer and exchange rings

In this paper, we prove that every element in an exchange ring r with artinian primitive factors is n-tuplet-good iff 1r is n-tuplet-good. also, we show that for such rings the full matrix ring mn(r) (for n ≥ 2) is n-tuplet-good. in [7], fisher and snider proved that every element of a strongly π-regular ring r with 1/2 ∈ r is 2-good. we prove the same result under new condition and show that these rings are twin-good. we also consider the conditions under which endomorphism ring of a finitely generated projective module m over unit regular ring l is 2-tuplet-good. the main result of [14] states that regular self-injective rings are n-tuplet-good if such rings has no factor ring isomorphic to a field d with |d| < n+2. we generalized this result to regular baer rings proving that every regular baer ring r that has no factor ring isomorphic to a field of order less than n + 2, is n-tuplet-good.