Ashish Srivastava: Rings Generated By Units

Abstract: A classical result of Zelinski states that every linear transformation on a vector space V, except when V is one-dimensional over Z_2, is a sum of two invertible linear transformations. We extend this result to any right self-injective ring R by proving that every element of R is a sum of two units if and only if no factor ring of R is isomorphic to Z_2. We also give a complete characterization of unit sum numbers of right self-injective rings.