^{1}Semnan UniversityFaculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.

^{2}Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran.

Receive Date: 04 November 2013,
Revise Date: 10 February 2015,
Accept Date: 10 February 2015

Abstract

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 $Z_2$ 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.

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