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 ۱_R is n-tuplet-good. Also, we show that for such rings the full matrix ring M_n(R) (for n\geq ۲) is n-tuplet-good. In [۷], Fisher and Snider proved that every element of a strongly \pi-regular ring R with \frac{۱}{۲}\in R is ۲-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 ۲-tuplet-good. The main result of [۱۴] states that regular self-injective rings are n-tuplet-good if such rings has no factor ring isomorphic to a field D with |D|Baer ring R that has no factor ring isomorphic to a field of order less than n+۲, is n-tuplet-good.

Keywords:

Baer ring , Exchange ring , n-tuplet-good ring , Strongly pi-regular ring , Twin-good ring