Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401The unit sum number of Baer rings427434769ENN.AshrafiSemnan UniversityFaculty of Mathematics, Statistics and
Computer Science,
Semnan University, Semnan, Iran.N.PouyanFaculty of Mathematics, Statistics and Computer Science,
Semnan
University, Semnan, Iran.Journal Article20131104In 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 <br />to $Z_2$ 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.http://bims.iranjournals.ir/article_769_b7f142c271337a1f63d0a503031cec1d.pdf