2-GOOD RINGS

A ring R is said to be k-good if every element is the sum of k units. We show that the endomorphism ring of a free module of rank at least 2 is 3-good and that every ring can be embedded in a 2-good ring. Answering a question of Skornjakov, we show that a (right) self-injective von Neumann regular ring is 2-good provided it has no 2-torsion. This generalizes a result of Zelinsky's on the ring of linear transformations of a vector space.