The unit sum number of Baer rings

‎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 ‎$\mathbb Z_2$ and we characterize regular Baer rings with unit sum‎ ‎numbers $\omega$ and $\infty$‎. ‎Then as an application‎, ‎we discuss‎ ‎the unit sum number of some classes of group rings.