A class of rings with the 2-sum property

Recall that a ring satisfies the 2-sum property if each of its elements is a sum of two units. Here a ring R is said to satisfy the binary 2-sum property if, for any a , b in R , there exists a unit u of R such that both a - u and b - u are units. A well-known result, due to Goldsmith, Pabst and Scot, states that a semilocal ring satisfies the 2-sum property iff it has no image isomorphic to Z 2 . It is proved here that a semilocal ring satisfies the binary 2-sum property iff it has no image isomorphic to Z 2 or Z 3 or M 2 ( Z 2 ) .