DECOMPOSING ELEMENTS OF A REGULAR BAER RING

: In this paper we prove that each element of any regular Baer ring is a sum of two units if no factor ring of R is isomorphic to Z2. Also we show this result for some classes of π-regular Baer rings. The main result of [14] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every element of a regular Baer ring is twin-good if and only if R has no factor ring isomorphic to Z2 or Z3.